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"file": "bounds/H3-m3-lower-4.json", "orbit": "H3", "m": 3, "direction": "lower", "rank": 4, "tier": "reproduced", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": "certs/H3-m3-lower-4.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_h3_m3_rank3.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.05, "wall_clock_hours": 0.05, "runs": 1, "hardware": "Apple silicon laptop, 8 worker processes" } }, { "slug": "H3-m3-upper-4", "file": "bounds/H3-m3-upper-4.json", "orbit": "H3", "m": 3, "direction": "upper", "rank": 4, "tier": "lean", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": null, "receipt_matches": null, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.M3StabRank", "lean_theorem": "h3_m3_stabRank_le_four", "lean_receipt": "certs/lean-LeanProofs-M3StabRank.json", "lean_receipt_ok": true, "compute": null }, { "slug": "H3-m4-lower-3", "file": "bounds/H3-m4-lower-3.json", "orbit": "H3", "m": 4, "direction": "lower", "rank": 3, "tier": "reproduced", "ok": true, "date": "2026-09-18", "author": "this repository", "reference": "stabrank rank_exclusion_codes.py", "method": "rank-2 exclusion over all 7,439,040 four-qutrit stabilizer states, held as phase codes", "pull_request": 38, "merge_commit": "b01a821f928b298e5adf701170ef8be02d448378", "merge_date": "2026-09-18", "added_commit": "b6b7739eb8115dc936ffbcbf4276dfa790524b11", "added_date": "2026-09-18", "added_subject": "chi(N^4) >= 3 and chi(H3^4) >= 3 in two minutes, superseding PR #20", "receipt": "certs/H3-m4-lower-3.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_h3_m4_rank2.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.05, "wall_clock_hours": 0.03, "runs": 1, "hardware": "Apple silicon laptop, one core" } }, { "slug": "H3-m4-lower-5", "file": "bounds/H3-m4-lower-5.json", "orbit": "H3", "m": 4, "direction": "lower", "rank": 5, "tier": "reproduced", "ok": true, "date": "2026-09-18", "author": "this repository", "reference": "stabrank slice_lift.py", "method": "slice-and-lift: the single rank-4 decomposition of |H3>^3 up to symmetry does not extend to |H3>^4", "pull_request": 55, "merge_commit": "517edd3c5b9955575fbc09076f9a539af718fa62", "merge_date": "2026-09-18", "added_commit": "0376132f65d7f960b5de58664273bc9609ab65d8", "added_date": "2026-09-18", "added_subject": "chi(H3^4) >= 5 by slice-and-lift", "receipt": "certs/H3-m4-lower-5.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_h3_m4_lift.py", "certificate_budget_s": 3600, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 1.4, "wall_clock_hours": 0.35, "runs": 1, "hardware": "Apple silicon laptop, four workers at low priority under a load average near 12: 1183 s for the enumeration and lift" } }, { "slug": "H3-m4-lower-6", "file": "bounds/H3-m4-lower-6.json", "orbit": "H3", "m": 4, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-09-23", "author": "this repository", "reference": "stabrank research/qutrit_m4_rank5", "method": "two-qutrit all-visible base slice: every rank-5 decomposition of |H3>^4 is carried by a monomial symmetry of |H3> on qutrits 1, 2 to one whose slice at x_0 = (1, 1) has all five terms nonzero (Facts A and B of the note), so that slice is a full 5-cover of |H3>^2; every such cover is enumerated up to the unitary symmetry of |H3>^2 and completed slice by slice under the two-qutrit slice structure lemma, modulo 65521 with exact re-decision", "pull_request": 118, "merge_commit": "ae2c6b993ad09768db0ebd85dcb77d2672e55343", "merge_date": "2026-09-23", "added_commit": "aea775a1e2f2a763047752fd71ed30f5632f18a1", "added_date": "2026-09-23", "added_subject": "chi(H3^4) >= 6: the rank-5 exclusion run, its batch manifest, and the attested bound", "receipt": "certs/H3-m4-lower-6.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_h3_m4_rank5_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/qutrit_m4_rank5/batch_manifest_H3.json", "recomputed": 2, "compute_hours": 11.2, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host (load 20 to 30), fifteen batches in parallel at nice 19, 2026-09-23 14:25 to 15:31 UTC; the aggregate's two seeded re-runs (batches 39 and 56, 773 s and 1,281 s) on the same pod, 2026-09-23 15:36 to 16:11 UTC", "note": "The exclusion of every rank-5 decomposition of |H3>^4 lives in the 57 stored batch outputs under research/qutrit_m4_rank5/results/H3/ (9 stage A batches over the 188,451 full 5-covers of |H3>^2 with distinct independent base states, 44 stage B batches over the 6,112 dependent covers, 4 stage C batches over the 7,024 covers with a repeated state, including the cancel-at-base multisets T + (b, b)), 201,587 covers matched at the base point x_0 = (1, 1) along qutrits 1, 2, every candidate re-decided mod 2013265921 and numerically, 0 hits, 0 refused, 0 undecided. The certificate checks the partition against the enumerator, re-enumerates the degenerate covers, verifies the hashes and geometry of every output, re-decides every stored hit, fails on any refusal or undecided run, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/qutrit_m4_rank5/batch.py, which regenerates any batch (batch.py H3 K).", "total": 57 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 11.2, "wall_clock_hours": 1.7, "runs": 1, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host (load 20 to 30), fifteen batches in parallel at nice 19, 2026-09-23 14:25 to 15:31 UTC; the aggregate's two seeded re-runs (batches 39 and 56, 773 s and 1,281 s) on the same pod, 2026-09-23 15:36 to 16:11 UTC" } }, { "slug": "H3-m4-lower-7", "file": "bounds/H3-m4-lower-7.json", "orbit": "H3", "m": 4, "direction": "lower", "rank": 7, "tier": "attested", "ok": true, "date": "2026-10-02", "author": "this repository", "reference": "stabrank research/h3_m4_rank6", "method": "two-qutrit base slice at (0, 0): every rank-6 decomposition of |H3>^4 has four, five or six terms visible at that point (Fact B of PR #86), so its base is a full 4-, 5- or 6-multiset of |H3>^2 and the invisible terms lie on the 16 flats missing (0, 0); every base is enumerated up to the unitary symmetry of |H3>^2 and completed slice by slice under the two-qutrit slice structure lemma, modulo 65521 with exact re-decision", "pull_request": 161, "merge_commit": "d3d386edcbc7168e579241ea12b4a24e1203f899", "merge_date": "2026-10-15", "added_commit": "5797ab339cc18914067df80a05cb0e311814c0de", "added_date": "2026-10-01", "added_subject": "chi(H3^4) >= 7 at the attested tier: the pod run of the rank-6 exclusion, its records, and the bound", "receipt": "certs/H3-m4-lower-7.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_h3_m4_rank6_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/h3_m4_rank6/batch_manifest.json", "recomputed": 2, "compute_hours": 81.5, "hardware": "RunPod CPU pod ee4072210b09 (32 vCPU, Ubuntu 20.04, gcc-10 kernels, Python 3.13.5, numpy 2.4.4), 28 batches in parallel at nice 19 alongside another job's 30 workers, 2026-10-01 18:14 to 2026-10-02 00:58 UTC for the 1,021-batch loop (81.1 CPU-hours of batch records: A6 14.6, B6 60.9, C6 3.3, beta' 2.3, gamma 0.03); the four heaviest stage A6 batches (0, 3, 4, 5, the pivot-117 pairs with 0.7 to 2.1 million covers each) were starved of CPU by an external SIGSTOP in the first pass (40 to 146 s of CPU in 4,740 s of wall) and recorded their covers as undecided at the 3,600 s wall-clock deadline, so they were re-run without a deadline 00:32 to 00:58 UTC (9 to 26 minutes each, 0 hits) and their records replace the starved ones; the aggregate (1,331 s, the 6-cover census re-run over every pivot pair and the lists re-enumerated, every count equal) and its two seeded re-runs (batches 142 and 1009, seed 20261002, 183 s and 157 s, deterministic hashes equal) on the same pod 01:03 to 01:25 UTC", "note": "The exclusion of every rank-6 decomposition of |H3>^4 lives in the stored batch outputs under research/h3_m4_rank6/results/ (88 stage A6 batches over the 36,368,678 full 6-covers of |H3>^2 with distinct independent base states, 802 stage B6 batches over the 378,843 G_2 orbit representatives of the dependent 6-sets, 92 stage C6 batches over the 354,012 representatives of the repeated 6-multisets, 36 stage beta' batches over the 61,413 representatives of the full 5-multisets with the invisible term on each of the 16 flats missing (0, 0), 3 stage gamma batches over the 565 representatives of the full 4-multisets with each of the 136 flat multisets), every base matched at x_0 = (0, 0) along qutrits 1, 2, every candidate re-decided mod 2013265921 and numerically, 0 hits, 0 refused, 0 undecided. The certificate checks the partition against the enumerator, re-runs the 6-cover kernel over every pivot pair, re-enumerates the orbit representatives, verifies the hashes and geometry of every output, re-decides every stored hit, fails on any refusal or undecided run, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/h3_m4_rank6/batch.py, which regenerates any batch (batch.py K).", "total": 1021 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 81.5, "wall_clock_hours": 7.2, "runs": 1, "hardware": "RunPod CPU pod ee4072210b09 (32 vCPU, Ubuntu 20.04, gcc-10 kernels, Python 3.13.5, numpy 2.4.4), 28 batches in parallel at nice 19 alongside another job's 30 workers, 2026-10-01 18:14 to 2026-10-02 00:58 UTC for the 1,021-batch loop (81.1 CPU-hours of batch records: A6 14.6, B6 60.9, C6 3.3, beta' 2.3, gamma 0.03); the four heaviest stage A6 batches (0, 3, 4, 5, the pivot-117 pairs with 0.7 to 2.1 million covers each) were starved of CPU by an external SIGSTOP in the first pass (40 to 146 s of CPU in 4,740 s of wall) and recorded their covers as undecided at the 3,600 s wall-clock deadline, so they were re-run without a deadline 00:32 to 00:58 UTC (9 to 26 minutes each, 0 hits) and their records replace the starved ones; the aggregate (1,331 s, the 6-cover census re-run over every pivot pair and the lists re-enumerated, every count equal) and its two seeded re-runs (batches 142 and 1009, seed 20261002, 183 s and 157 s, deterministic hashes equal) on the same pod 01:03 to 01:25 UTC" } }, { "slug": "H3-m4-upper-8", "file": "bounds/H3-m4-upper-8.json", "orbit": "H3", "m": 4, "direction": "upper", "rank": 8, "tier": "lean", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": "certs/H3-m4-upper-8.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.H3M4StabRank", "lean_theorem": "h3_m4_stabRankP_le_eight", "lean_receipt": "certs/lean-LeanProofs-H3M4StabRank.json", "lean_receipt_ok": true, "compute": null }, { "slug": "H3-m5-lower-7", "file": "bounds/H3-m5-lower-7.json", "orbit": "H3", "m": 5, "direction": "lower", "rank": 7, "tier": "attested", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank research/h3_m4_rank6", "method": "projection monotonicity applied to the attested exact rank-6 exclusion at m=4", "pull_request": 179, "merge_commit": "0ee13cc9fc34e8295fa70fed697e4da63f470a1b", "merge_date": "2026-10-21", "added_commit": "97e913306bded234bbee81b811e44fc39c075773", "added_date": "2026-10-21", "added_subject": "Carry the H3 lower bound to m = 5 and 6 by projection monotonicity", "receipt": "certs/H3-m5-lower-7.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_h3_m4_rank6_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/h3_m4_rank6/batch_manifest.json", "recomputed": 2, "compute_hours": 81.5, "hardware": "RunPod CPU pod ee4072210b09 (32 vCPU, Ubuntu 20.04, gcc-10 kernels, Python 3.13.5, numpy 2.4.4), 28 batches in parallel at nice 19 alongside another job's 30 workers, 2026-10-01 18:14 to 2026-10-02 00:58 UTC for the 1,021-batch loop (81.1 CPU-hours of batch records: A6 14.6, B6 60.9, C6 3.3, beta' 2.3, gamma 0.03); the four heaviest stage A6 batches (0, 3, 4, 5, the pivot-117 pairs with 0.7 to 2.1 million covers each) were starved of CPU by an external SIGSTOP in the first pass (40 to 146 s of CPU in 4,740 s of wall) and recorded their covers as undecided at the 3,600 s wall-clock deadline, so they were re-run without a deadline 00:32 to 00:58 UTC (9 to 26 minutes each, 0 hits) and their records replace the starved ones; the aggregate (1,331 s, the 6-cover census re-run over every pivot pair and the lists re-enumerated, every count equal) and its two seeded re-runs (batches 142 and 1009, seed 20261002, 183 s and 157 s, deterministic hashes equal) on the same pod 01:03 to 01:25 UTC", "note": "The exclusion of every rank-6 decomposition of |H3>^4 lives in the stored batch outputs under research/h3_m4_rank6/results/ (88 stage A6 batches over the 36,368,678 full 6-covers of |H3>^2 with distinct independent base states, 802 stage B6 batches over the 378,843 G_2 orbit representatives of the dependent 6-sets, 92 stage C6 batches over the 354,012 representatives of the repeated 6-multisets, 36 stage beta' batches over the 61,413 representatives of the full 5-multisets with the invisible term on each of the 16 flats missing (0, 0), 3 stage gamma batches over the 565 representatives of the full 4-multisets with each of the 136 flat multisets), every base matched at x_0 = (0, 0) along qutrits 1, 2, every candidate re-decided mod 2013265921 and numerically, 0 hits, 0 refused, 0 undecided. The certificate checks the partition against the enumerator, re-runs the 6-cover kernel over every pivot pair, re-enumerates the orbit representatives, verifies the hashes and geometry of every output, re-decides every stored hit, fails on any refusal or undecided run, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/h3_m4_rank6/batch.py, which regenerates any batch (batch.py K).", "total": 1021 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=4 certificate, which this cell re-runs" } }, { "slug": "H3-m5-upper-12", "file": "bounds/H3-m5-upper-12.json", "orbit": "H3", "m": 5, "direction": "upper", "rank": 12, "tier": "verified", "ok": true, "date": "2026-09-23", "author": "this repository", "reference": "stabrank research/constructions/product_witness.py", "method": "structured construction", "pull_request": 115, "merge_commit": "2ce2188bcde0855200b915c35bedefc598af266a", "merge_date": "2026-09-23", "added_commit": "bd2b13d4cf153ba9321cfa2faf4143e5c8472ba3", "added_date": "2026-09-23", "added_subject": "Sweep of 2026-09-23: T5 and qutrit product witnesses, a T5 m=2 rank-7 search, literature update", "receipt": "certs/H3-m5-upper-12.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "H3-m6-lower-7", "file": "bounds/H3-m6-lower-7.json", "orbit": "H3", "m": 6, "direction": "lower", "rank": 7, "tier": "attested", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank research/h3_m4_rank6", "method": "projection monotonicity applied to the attested exact rank-6 exclusion at m=4", "pull_request": 179, "merge_commit": "0ee13cc9fc34e8295fa70fed697e4da63f470a1b", "merge_date": "2026-10-21", "added_commit": "97e913306bded234bbee81b811e44fc39c075773", "added_date": "2026-10-21", "added_subject": "Carry the H3 lower bound to m = 5 and 6 by projection monotonicity", "receipt": "certs/H3-m6-lower-7.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_h3_m4_rank6_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/h3_m4_rank6/batch_manifest.json", "recomputed": 2, "compute_hours": 81.5, "hardware": "RunPod CPU pod ee4072210b09 (32 vCPU, Ubuntu 20.04, gcc-10 kernels, Python 3.13.5, numpy 2.4.4), 28 batches in parallel at nice 19 alongside another job's 30 workers, 2026-10-01 18:14 to 2026-10-02 00:58 UTC for the 1,021-batch loop (81.1 CPU-hours of batch records: A6 14.6, B6 60.9, C6 3.3, beta' 2.3, gamma 0.03); the four heaviest stage A6 batches (0, 3, 4, 5, the pivot-117 pairs with 0.7 to 2.1 million covers each) were starved of CPU by an external SIGSTOP in the first pass (40 to 146 s of CPU in 4,740 s of wall) and recorded their covers as undecided at the 3,600 s wall-clock deadline, so they were re-run without a deadline 00:32 to 00:58 UTC (9 to 26 minutes each, 0 hits) and their records replace the starved ones; the aggregate (1,331 s, the 6-cover census re-run over every pivot pair and the lists re-enumerated, every count equal) and its two seeded re-runs (batches 142 and 1009, seed 20261002, 183 s and 157 s, deterministic hashes equal) on the same pod 01:03 to 01:25 UTC", "note": "The exclusion of every rank-6 decomposition of |H3>^4 lives in the stored batch outputs under research/h3_m4_rank6/results/ (88 stage A6 batches over the 36,368,678 full 6-covers of |H3>^2 with distinct independent base states, 802 stage B6 batches over the 378,843 G_2 orbit representatives of the dependent 6-sets, 92 stage C6 batches over the 354,012 representatives of the repeated 6-multisets, 36 stage beta' batches over the 61,413 representatives of the full 5-multisets with the invisible term on each of the 16 flats missing (0, 0), 3 stage gamma batches over the 565 representatives of the full 4-multisets with each of the 136 flat multisets), every base matched at x_0 = (0, 0) along qutrits 1, 2, every candidate re-decided mod 2013265921 and numerically, 0 hits, 0 refused, 0 undecided. The certificate checks the partition against the enumerator, re-runs the 6-cover kernel over every pivot pair, re-enumerates the orbit representatives, verifies the hashes and geometry of every output, re-decides every stored hit, fails on any refusal or undecided run, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/h3_m4_rank6/batch.py, which regenerates any batch (batch.py K).", "total": 1021 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=4 certificate, which this cell re-runs" } }, { "slug": "H3-m6-upper-16", "file": "bounds/H3-m6-upper-16.json", "orbit": "H3", "m": 6, "direction": "upper", "rank": 16, "tier": "verified", "ok": true, "date": "2026-09-23", "author": "this repository", "reference": "stabrank research/constructions/product_witness.py", "method": "structured construction", "pull_request": 115, "merge_commit": "2ce2188bcde0855200b915c35bedefc598af266a", "merge_date": "2026-09-23", "added_commit": "bd2b13d4cf153ba9321cfa2faf4143e5c8472ba3", "added_date": "2026-09-23", "added_subject": "Sweep of 2026-09-23: T5 and qutrit product witnesses, a T5 m=2 rank-7 search, literature update", "receipt": "certs/H3-m6-upper-16.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "N-m1-lower-2", "file": "bounds/N-m1-lower-2.json", "orbit": "N", "m": 1, "direction": "lower", "rank": 2, "tier": "verified", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank verify_challenge", "method": "exact: the state is not a stabilizer state (the moduli 1/sqrt6 and 2/sqrt6 differ)", "pull_request": 177, "merge_commit": "2fffdf2d28dafba398e4162820f9df00b1eefefb", "merge_date": "2026-10-21", "added_commit": "dd232c348dfd99d3339e2e11dcad6749b7bc27e9", "added_date": "2026-10-21", "added_subject": "File the single-copy cells of H3, N, qubit_H, and qubit_T", "receipt": "certs/N-m1-lower-2.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_rank1_moduli.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": null }, { "slug": "N-m1-upper-2", "file": "bounds/N-m1-upper-2.json", "orbit": "N", "m": 1, "direction": "upper", "rank": 2, "tier": "verified", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank research/constructions/data", "method": "direct construction: the single-copy state as a combination of two stabilizer states", "pull_request": 177, "merge_commit": "2fffdf2d28dafba398e4162820f9df00b1eefefb", "merge_date": "2026-10-21", "added_commit": "dd232c348dfd99d3339e2e11dcad6749b7bc27e9", "added_date": "2026-10-21", "added_subject": "File the single-copy cells of H3, N, qubit_H, and qubit_T", "receipt": "certs/N-m1-upper-2.json", "receipt_matches": true, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "N-m2-lower-3", "file": "bounds/N-m2-lower-3.json", "orbit": "N", "m": 2, "direction": "lower", "rank": 3, "tier": "lean", "ok": true, "date": "2026-09-12", "author": "this repository", "reference": "stabrank PR #18", "method": "exhaustion over all 64620 pairs of 2-qutrit stabilizer states", "pull_request": 18, "merge_commit": "293f15c35bdf189751f6e2b8cf833f535d04f287", "merge_date": "2026-09-16", "added_commit": "b53bead597f5373a3e246316902c18b9dbc7054d", "added_date": "2026-09-12", "added_subject": "Certify chi(N^2) >= 3 and chi(H3^2) >= 3", "receipt": "certs/N-m2-lower-3.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_m2_rank2.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.M2Lower", "lean_theorem": "norrell_m2_stabRank_gt_two", "lean_receipt": "certs/lean-LeanProofs-M2Lower.json", "lean_receipt_ok": true, "compute": null }, { "slug": "N-m2-upper-3", "file": "bounds/N-m2-upper-3.json", "orbit": "N", "m": 2, "direction": "upper", "rank": 3, "tier": "lean", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": null, "receipt_matches": null, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.M2StabRank", "lean_theorem": "norrell_m2_stabRank_le_three", "lean_receipt": "certs/lean-LeanProofs-M2StabRank.json", "lean_receipt_ok": true, "compute": null }, { "slug": "N-m3-lower-4", "file": "bounds/N-m3-lower-4.json", "orbit": "N", "m": 3, "direction": "lower", "rank": 4, "tier": "reproduced", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": "certs/N-m3-lower-4.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_n_m3_rank3.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.05, "wall_clock_hours": 0.05, "runs": 1, "hardware": "Apple silicon laptop, 8 worker processes" } }, { "slug": "N-m3-upper-4", "file": "bounds/N-m3-upper-4.json", "orbit": "N", "m": 3, "direction": "upper", "rank": 4, "tier": "lean", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": null, "receipt_matches": null, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.M3StabRank", "lean_theorem": "norrell_m3_stabRank_le_four", "lean_receipt": "certs/lean-LeanProofs-M3StabRank.json", "lean_receipt_ok": true, "compute": null }, { "slug": "N-m4-lower-3", "file": "bounds/N-m4-lower-3.json", "orbit": "N", "m": 4, "direction": "lower", "rank": 3, "tier": "reproduced", "ok": true, "date": "2026-09-18", "author": "this repository", "reference": "stabrank rank_exclusion_codes.py", "method": "rank-2 exclusion over all 7,439,040 four-qutrit stabilizer states, held as phase codes", "pull_request": 38, "merge_commit": "b01a821f928b298e5adf701170ef8be02d448378", "merge_date": "2026-09-18", "added_commit": "b6b7739eb8115dc936ffbcbf4276dfa790524b11", "added_date": "2026-09-18", "added_subject": "chi(N^4) >= 3 and chi(H3^4) >= 3 in two minutes, superseding PR #20", "receipt": "certs/N-m4-lower-3.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_n_m4_rank2.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.05, "wall_clock_hours": 0.03, "runs": 1, "hardware": "Apple silicon laptop, one core" } }, { "slug": "N-m4-lower-5", "file": "bounds/N-m4-lower-5.json", "orbit": "N", "m": 4, "direction": "lower", "rank": 5, "tier": "reproduced", "ok": true, "date": "2026-09-18", "author": "this repository", "reference": "stabrank slice_lift.py", "method": "slice-and-lift: the single rank-4 decomposition of |N>^3 up to symmetry does not extend to |N>^4", "pull_request": 42, "merge_commit": "4c0d35fc401543fb9201713d805310ca2674d3d5", "merge_date": "2026-09-18", "added_commit": "fc5587f4bbe0b23eea27e265d256c7c4a1c318ed", "added_date": "2026-09-18", "added_subject": "chi(N^4) >= 5 by slice-and-lift, the first cell on a declared budget", "receipt": "certs/N-m4-lower-5.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_n_m4_lift.py", "certificate_budget_s": 3600, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 7.6, "wall_clock_hours": 7.6, "runs": 3, "hardware": "Apple silicon laptop at low priority for the 6.4-hour first enumeration; the certificate ran in 43 minutes on the 4-core CI runner with the numpy search, and re-runs here with the compiled kernel" } }, { "slug": "N-m4-lower-6", "file": "bounds/N-m4-lower-6.json", "orbit": "N", "m": 4, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-09-23", "author": "this repository", "reference": "stabrank research/qutrit_m4_rank5", "method": "two-qutrit all-visible base slice: every rank-5 decomposition of |N>^4 is carried by a monomial symmetry of |N> on qutrits 1, 2 to one whose slice at x_0 = (0, 0) has all five terms nonzero (Facts A and B of the note), so that slice is a full 5-cover of |N>^2; every such cover is enumerated up to the unitary symmetry of |N>^2 and completed slice by slice under the two-qutrit slice structure lemma, modulo 65521 with exact re-decision", "pull_request": 120, "merge_commit": "5e37ed6f9fb06456cde5f5110f4dabf8c4bb5f2d", "merge_date": "2026-09-23", "added_commit": "cd2591e76edfac06a43cbdfa3bee9b830265f5bd", "added_date": "2026-09-23", "added_subject": "chi(N^4) >= 6: the rank-5 exclusion run, its batch manifest, and the attested bound", "receipt": "certs/N-m4-lower-6.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_n_m4_rank5_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/qutrit_m4_rank5/batch_manifest_N.json", "recomputed": 2, "compute_hours": 38.1, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host (load 20 to 30), fifteen batches in parallel at nice 19, 2026-09-23 14:25 to 18:08 UTC (three sample batches at 14:25, the 141 shared batches 15:31 to 17:34, the 27 single-cover stage C batches 17:34 to 18:08); the aggregate's two seeded re-runs (batches 121 and 169, 720 s and 583 s) on the same pod, 2026-09-23 18:50 to 19:12 UTC", "note": "The exclusion of every rank-5 decomposition of |N>^4 lives in the 171 stored batch outputs under research/qutrit_m4_rank5/results/N/ (17 stage A batches over the 197,440 full 5-covers of |N>^2 with distinct independent base states, 98 stage B batches over the 12,175 dependent covers, 56 stage C batches over the 16,181 covers with a repeated state, including the cancel-at-base multisets T + (b, b) and the 27 covers with two blocks in one Pauli orbit, each alone in its batch), 225,796 covers matched at the base point x_0 = (0, 0) along qutrits 1, 2, every candidate re-decided mod 2013265921 and numerically, 0 hits, 0 refused, 0 undecided. The certificate checks the partition against the enumerator, re-enumerates the degenerate covers, verifies the hashes and geometry of every output, re-decides every stored hit, fails on any refusal or undecided run, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/qutrit_m4_rank5/batch.py, which regenerates any batch (batch.py N K).", "total": 171 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 38.1, "wall_clock_hours": 4.1, "runs": 1, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host (load 20 to 30), fifteen batches in parallel at nice 19, 2026-09-23 14:25 to 18:08 UTC (three sample batches at 14:25, the 141 shared batches 15:31 to 17:34, the 27 single-cover stage C batches 17:34 to 18:08); the aggregate's two seeded re-runs (batches 121 and 169, 720 s and 583 s) on the same pod, 2026-09-23 18:50 to 19:12 UTC" } }, { "slug": "N-m4-lower-7", "file": "bounds/N-m4-lower-7.json", "orbit": "N", "m": 4, "direction": "lower", "rank": 7, "tier": "attested", "ok": true, "date": "2026-09-26", "author": "this repository", "reference": "stabrank research/n4_rank6", "method": "two-qutrit base slice at (2, 2): every rank-6 decomposition of |N>^4 has four, five or six terms visible at that point (Fact B of PR #86), so its base is a full 4-, 5- or 6-multiset of |N>^2 and the invisible terms lie on the 16 flats missing (2, 2); every base is enumerated up to the unitary symmetry of |N>^2 and completed slice by slice under the two-qutrit slice structure lemma, modulo 65521 with exact re-decision", "pull_request": 154, "merge_commit": "01da020f7c8e8425e0515c183b8c03aa61b411f9", "merge_date": "2026-09-26", "added_commit": "73931444d82d93dcc777f011b4391a5071a13a58", "added_date": "2026-09-26", "added_subject": "chi(N^4) >= 7: the rank-6 exclusion run, its batch manifest, and the attested bound", "receipt": "certs/N-m4-lower-7.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_n_m4_rank6_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/n4_rank6/batch_manifest.json", "recomputed": 2, "compute_hours": 121.5, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host, fifteen batches in parallel at nice 19 (gcc-10 kernels, Python 3.12, numpy 2.3.5), 2026-09-25 21:04 to 2026-09-26 05:40 UTC for the 1,057-batch loop; the 23 stage B6 batches whose 24 items the first aggregate left undecided (the fresh-term filter of PR #153) rerun with --force on the same pod 06:12 to 06:26 UTC; the aggregate's two seeded re-runs (batches 168 and 799, seed 20260925, 255 s and 283 s) on the same pod at 06:26 to 06:46 UTC; the --no-native replays of batches 53 and 764 (05:50 to 09:22 UTC, deterministic hashes equal to the stored ones) under research/n4_rank6/results/nonative/", "note": "The exclusion of every rank-6 decomposition of |N>^4 lives in the stored batch outputs under research/n4_rank6/results/ (54 stage A6 batches over the 37,201,212 full 6-covers of |N>^2 with distinct independent base states, 807 stage B6 batches over the 259,655 G_2 orbit representatives of the dependent 6-sets, 166 stage C6 batches over the 321,553 representatives of the repeated 6-multisets, 27 stage beta' batches over the 54,488 representatives of the full 5-multisets with the invisible term on each of the 16 flats missing (2, 2), 3 stage gamma batches over the 505 representatives of the full 4-multisets with each of the 136 flat multisets), every base matched at x_0 = (2, 2) along qutrits 1, 2, every candidate re-decided mod 2013265921 and numerically, 0 hits, 0 refused, 0 undecided. The certificate checks the partition against the enumerator, re-runs the 6-cover kernel over every pivot pair, re-enumerates the orbit representatives, verifies the hashes and geometry of every output, re-decides every stored hit, fails on any refusal or undecided run, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/n4_rank6/batch.py, which regenerates any batch (batch.py K).", "total": 1057 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 121.5, "wall_clock_hours": 9.7, "runs": 1, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host, fifteen batches in parallel at nice 19 (gcc-10 kernels, Python 3.12, numpy 2.3.5), 2026-09-25 21:04 to 2026-09-26 05:40 UTC for the 1,057-batch loop; the 23 stage B6 batches whose 24 items the first aggregate left undecided (the fresh-term filter of PR #153) rerun with --force on the same pod 06:12 to 06:26 UTC; the aggregate's two seeded re-runs (batches 168 and 799, seed 20260925, 255 s and 283 s) on the same pod at 06:26 to 06:46 UTC; the --no-native replays of batches 53 and 764 (05:50 to 09:22 UTC, deterministic hashes equal to the stored ones) under research/n4_rank6/results/nonative/" } }, { "slug": "N-m4-upper-7", "file": "bounds/N-m4-upper-7.json", "orbit": "N", "m": 4, "direction": "upper", "rank": 7, "tier": "lean", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": null, "receipt_matches": null, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.M4StabRank", "lean_theorem": "norrell_m4_stabRank_le_seven", "lean_receipt": "certs/lean-LeanProofs-M4StabRank.json", "lean_receipt_ok": true, "compute": null }, { "slug": "N-m5-lower-7", "file": "bounds/N-m5-lower-7.json", "orbit": "N", "m": 5, "direction": "lower", "rank": 7, "tier": "attested", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank research/n4_rank6", "method": "projection monotonicity applied to the attested exact rank-6 exclusion at m=4", "pull_request": 180, "merge_commit": "1b6a01fbe9abb1709ed57e4f031aa20b2c8af78e", "merge_date": "2026-10-21", "added_commit": "ed338df27bf8ed405f9948770e477b8b8042d9eb", "added_date": "2026-10-21", "added_subject": "Carry the N lower bound to m = 5 and 6 by projection monotonicity", "receipt": "certs/N-m5-lower-7.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_n_m4_rank6_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/n4_rank6/batch_manifest.json", "recomputed": 2, "compute_hours": 121.5, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host, fifteen batches in parallel at nice 19 (gcc-10 kernels, Python 3.12, numpy 2.3.5), 2026-09-25 21:04 to 2026-09-26 05:40 UTC for the 1,057-batch loop; the 23 stage B6 batches whose 24 items the first aggregate left undecided (the fresh-term filter of PR #153) rerun with --force on the same pod 06:12 to 06:26 UTC; the aggregate's two seeded re-runs (batches 168 and 799, seed 20260925, 255 s and 283 s) on the same pod at 06:26 to 06:46 UTC; the --no-native replays of batches 53 and 764 (05:50 to 09:22 UTC, deterministic hashes equal to the stored ones) under research/n4_rank6/results/nonative/", "note": "The exclusion of every rank-6 decomposition of |N>^4 lives in the stored batch outputs under research/n4_rank6/results/ (54 stage A6 batches over the 37,201,212 full 6-covers of |N>^2 with distinct independent base states, 807 stage B6 batches over the 259,655 G_2 orbit representatives of the dependent 6-sets, 166 stage C6 batches over the 321,553 representatives of the repeated 6-multisets, 27 stage beta' batches over the 54,488 representatives of the full 5-multisets with the invisible term on each of the 16 flats missing (2, 2), 3 stage gamma batches over the 505 representatives of the full 4-multisets with each of the 136 flat multisets), every base matched at x_0 = (2, 2) along qutrits 1, 2, every candidate re-decided mod 2013265921 and numerically, 0 hits, 0 refused, 0 undecided. The certificate checks the partition against the enumerator, re-runs the 6-cover kernel over every pivot pair, re-enumerates the orbit representatives, verifies the hashes and geometry of every output, re-decides every stored hit, fails on any refusal or undecided run, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/n4_rank6/batch.py, which regenerates any batch (batch.py K).", "total": 1057 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=4 certificate, which this cell re-runs" } }, { "slug": "N-m5-upper-10", "file": "bounds/N-m5-upper-10.json", "orbit": "N", "m": 5, "direction": "upper", "rank": 10, "tier": "verified", "ok": true, "date": "2026-10-16", "author": "Vincent Russo", "reference": "this repository (stabrank-research, round 28 letter lifts)", "method": "sparsest word representation of |N>^5 over (four-ray stabilizer-spanned three-space through |N>^2) x (same) x (four-ray plane through |N>), HiGHS MILP, coefficients solved exactly over Q(omega_3)", "pull_request": 171, "merge_commit": "e6c9e5cb92c61576f0ce337c3777f8dbcc695dce", "merge_date": "2026-10-17", "added_commit": "9867cf065918033d9a5c6cbce51044c67ce8708f", "added_date": "2026-10-17", "added_subject": "chi(N^5) <= 10: a ten-term stabilizer decomposition of |N>^5 (verified tier)", "receipt": "certs/N-m5-upper-10.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 6, "wall_clock_hours": 5, "runs": 6, "hardware": "Apple silicon laptop, one core per solve; one confirming solve on a Perlmutter CPU node", "llm": [ { "model": "claude-fable-5-1", "role": "designed and ran the search and the exact refit" } ] } }, { "slug": "N-m5-upper-12", "file": "bounds/N-m5-upper-12.json", "orbit": "N", "m": 5, "direction": "upper", "rank": 12, "tier": "verified", "ok": true, "date": "2026-09-23", "author": "this repository", "reference": "stabrank research/constructions/product_witness.py", "method": "structured construction", "pull_request": 115, "merge_commit": "2ce2188bcde0855200b915c35bedefc598af266a", "merge_date": "2026-09-23", "added_commit": "bd2b13d4cf153ba9321cfa2faf4143e5c8472ba3", "added_date": "2026-09-23", "added_subject": "Sweep of 2026-09-23: T5 and qutrit product witnesses, a T5 m=2 rank-7 search, literature update", "receipt": "certs/N-m5-upper-12.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "N-m6-lower-7", "file": "bounds/N-m6-lower-7.json", "orbit": "N", "m": 6, "direction": "lower", "rank": 7, "tier": "attested", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank research/n4_rank6", "method": "projection monotonicity applied to the attested exact rank-6 exclusion at m=4", "pull_request": 180, "merge_commit": "1b6a01fbe9abb1709ed57e4f031aa20b2c8af78e", "merge_date": "2026-10-21", "added_commit": "ed338df27bf8ed405f9948770e477b8b8042d9eb", "added_date": "2026-10-21", "added_subject": "Carry the N lower bound to m = 5 and 6 by projection monotonicity", "receipt": "certs/N-m6-lower-7.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_n_m4_rank6_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/n4_rank6/batch_manifest.json", "recomputed": 2, "compute_hours": 121.5, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host, fifteen batches in parallel at nice 19 (gcc-10 kernels, Python 3.12, numpy 2.3.5), 2026-09-25 21:04 to 2026-09-26 05:40 UTC for the 1,057-batch loop; the 23 stage B6 batches whose 24 items the first aggregate left undecided (the fresh-term filter of PR #153) rerun with --force on the same pod 06:12 to 06:26 UTC; the aggregate's two seeded re-runs (batches 168 and 799, seed 20260925, 255 s and 283 s) on the same pod at 06:26 to 06:46 UTC; the --no-native replays of batches 53 and 764 (05:50 to 09:22 UTC, deterministic hashes equal to the stored ones) under research/n4_rank6/results/nonative/", "note": "The exclusion of every rank-6 decomposition of |N>^4 lives in the stored batch outputs under research/n4_rank6/results/ (54 stage A6 batches over the 37,201,212 full 6-covers of |N>^2 with distinct independent base states, 807 stage B6 batches over the 259,655 G_2 orbit representatives of the dependent 6-sets, 166 stage C6 batches over the 321,553 representatives of the repeated 6-multisets, 27 stage beta' batches over the 54,488 representatives of the full 5-multisets with the invisible term on each of the 16 flats missing (2, 2), 3 stage gamma batches over the 505 representatives of the full 4-multisets with each of the 136 flat multisets), every base matched at x_0 = (2, 2) along qutrits 1, 2, every candidate re-decided mod 2013265921 and numerically, 0 hits, 0 refused, 0 undecided. The certificate checks the partition against the enumerator, re-runs the 6-cover kernel over every pivot pair, re-enumerates the orbit representatives, verifies the hashes and geometry of every output, re-decides every stored hit, fails on any refusal or undecided run, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/n4_rank6/batch.py, which regenerates any batch (batch.py K).", "total": 1057 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=4 certificate, which this cell re-runs" } }, { "slug": "N-m6-upper-16", "file": "bounds/N-m6-upper-16.json", "orbit": "N", "m": 6, "direction": "upper", "rank": 16, "tier": "verified", "ok": true, "date": "2026-09-23", "author": "this repository", "reference": "stabrank research/constructions/product_witness.py", "method": "structured construction", "pull_request": 115, "merge_commit": "2ce2188bcde0855200b915c35bedefc598af266a", "merge_date": "2026-09-23", "added_commit": "bd2b13d4cf153ba9321cfa2faf4143e5c8472ba3", "added_date": "2026-09-23", "added_subject": "Sweep of 2026-09-23: T5 and qutrit product witnesses, a T5 m=2 rank-7 search, literature update", "receipt": "certs/N-m6-upper-16.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "S-m1-lower-2", "file": "bounds/S-m1-lower-2.json", "orbit": "S", "m": 1, "direction": "lower", "rank": 2, "tier": "lean", "ok": true, "date": "2026-09-20", "author": "this repository", "reference": "stabrank verify_challenge", "method": "exact: the state is not a stabilizer state (support size 2 is not an affine flat of F_3)", "pull_request": 61, "merge_commit": "fec578fb6ad236de4564d49145a619b4924bd963", "merge_date": "2026-09-20", "added_commit": "801680d49c63f74d82974b5bab3f9b566965b959", "added_date": "2026-09-20", "added_subject": "Lower bounds for the five cells that had none", "receipt": "certs/S-m1-lower-2.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_rank1_moduli.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.StrangeM1Lower", "lean_theorem": "strange_m1_stabRank_gt_one", "lean_receipt": "certs/lean-LeanProofs-StrangeM1Lower.json", "lean_receipt_ok": true, "compute": null }, { "slug": "S-m1-upper-2", "file": "bounds/S-m1-upper-2.json", "orbit": "S", "m": 1, "direction": "upper", "rank": 2, "tier": "lean", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": "certs/S-m1-upper-2.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.M1StabRank", "lean_theorem": "strange_m1_stabRank_le_two", "lean_receipt": "certs/lean-LeanProofs-M1StabRank.json", "lean_receipt_ok": true, "compute": null }, { "slug": "S-m2-lower-2", "file": "bounds/S-m2-lower-2.json", "orbit": "S", "m": 2, "direction": "lower", "rank": 2, "tier": "lean", "ok": true, "date": "2026-09-15", "author": "this repository", "reference": "stabrank PR #19", "method": "affine-support obstruction, formalized in Lean", "pull_request": 19, "merge_commit": "108ccb1d8afcd6a1ef3f43b954c67719849db9c7", "merge_date": "2026-09-16", "added_commit": "3ff6e746a811eb0dcda864cf02bb7e294187513f", "added_date": "2026-09-15", "added_subject": "First Lean lower bound, and a Lean proof for chi(T3^2) <= 3", "receipt": null, "receipt_matches": null, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.Stabilizer.IsStab", "lean_theorem": "strange_m2_stabRank_gt_one", "lean_receipt": "certs/lean-LeanProofs-Stabilizer-IsStab.json", "lean_receipt_ok": true, "compute": null }, { "slug": "S-m2-upper-2", "file": "bounds/S-m2-upper-2.json", "orbit": "S", "m": 2, "direction": "upper", "rank": 2, "tier": "lean", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586, Theorem 2", "method": "carry decomposition", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": null, "receipt_matches": null, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.Stabilizer.IsStab", "lean_theorem": "strange_m2_stabRank_le_two", "lean_receipt": "certs/lean-LeanProofs-Stabilizer-IsStab.json", "lean_receipt_ok": true, "compute": null }, { "slug": "S-m3-lower-4", "file": "bounds/S-m3-lower-4.json", "orbit": "S", "m": 3, "direction": "lower", "rank": 4, "tier": "reproduced", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": "certs/S-m3-lower-4.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_s_m3_rank3.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.05, "wall_clock_hours": 0.05, "runs": 1, "hardware": "Apple silicon laptop, 8 worker processes" } }, { "slug": "S-m3-upper-4", "file": "bounds/S-m3-upper-4.json", "orbit": "S", "m": 3, "direction": "upper", "rank": 4, "tier": "lean", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": null, "receipt_matches": null, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.M3StabRank", "lean_theorem": "strange_m3_stabRank_le_four", "lean_receipt": "certs/lean-LeanProofs-M3StabRank.json", "lean_receipt_ok": true, "compute": null }, { "slug": "S-m4-lower-4", "file": "bounds/S-m4-lower-4.json", "orbit": "S", "m": 4, "direction": "lower", "rank": 4, "tier": "reproduced", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": "certs/S-m4-lower-4.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_s_m4_from_m3.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": null }, { "slug": "S-m4-upper-4", "file": "bounds/S-m4-upper-4.json", "orbit": "S", "m": 4, "direction": "upper", "rank": 4, "tier": "lean", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": "certs/S-m4-upper-4.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.TensorStabRank", "lean_theorem": "strange_m4_stabRank_le_four", "lean_receipt": "certs/lean-LeanProofs-TensorStabRank.json", "lean_receipt_ok": true, "compute": null }, { "slug": "S-m5-lower-4", "file": "bounds/S-m5-lower-4.json", "orbit": "S", "m": 5, "direction": "lower", "rank": 4, "tier": "reproduced", "ok": true, "date": "2026-09-18", "author": "this repository", "reference": "stabrank rank_exclusion.py", "method": "projection monotonicity applied to an exhaustive exclusion at lower m", "pull_request": 37, "merge_commit": "8123be156aa8ee0394af17b6cc170fdbff894af3", "merge_date": "2026-09-18", "added_commit": "be6917e6b0b390196a355d6051beb3197ef043d7", "added_date": "2026-09-18", "added_subject": "Fill the S and BK T-type cells at m=5, both directions", "receipt": "certs/S-m5-lower-4.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_s_m5_from_m3.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.01, "wall_clock_hours": 0.005, "runs": 1, "hardware": "Apple silicon laptop" } }, { "slug": "S-m5-lower-5", "file": "bounds/S-m5-lower-5.json", "orbit": "S", "m": 5, "direction": "lower", "rank": 5, "tier": "reproduced", "ok": true, "date": "2026-09-18", "author": "this repository", "reference": "stabrank slice_lift.py", "method": "slice-and-lift twice: every rank-4 decomposition of |S>^3 up to symmetry, lifted to |S>^4, none extends to |S>^5", "pull_request": 40, "merge_commit": "a3d18db43a39d6fe00d2220e3c03e0ca30822be9", "merge_date": "2026-09-18", "added_commit": "f44f13ea8b1688f96ab04aee6eba4d3e6e1fa611", "added_date": "2026-09-18", "added_subject": "chi(S^5) >= 5 by slice-and-lift twice", "receipt": "certs/S-m5-lower-5.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_s_m5_lift.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 2.7, "wall_clock_hours": 2.6, "runs": 3, "hardware": "Apple silicon laptop at low priority; the first enumeration ran 2.2 hours on one core, the certificate takes about two minutes on four" } }, { "slug": "S-m5-lower-6", "file": "bounds/S-m5-lower-6.json", "orbit": "S", "m": 5, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-10-23", "author": "Vincent Russo", "reference": "stabrank-research, round 33 (attacks/round33-strange-rank5)", "method": "recursive slice-and-lift over non-minimal covers: every five-term decomposition of |S>^5 is all full, hence a lift of a five-term decomposition of |S>^4 with nonzero coefficients; these are lifts of five-covers of |S>^3 (exact census) or completions of its four-term decompositions; no level-4 base lifts", "pull_request": 187, "merge_commit": "b0cc69b9e71e0df1a170c7abbf0ce8e6858b8310", "merge_date": "2026-10-23", "added_commit": "b42f73cccc6ddc360166b9db24de892c624ee2a3", "added_date": "2026-10-23", "added_subject": "Strange state: chi(S^5) >= 6 by a complete recursive slice-and-lift over non-minimal covers (attested), carried to m = 6, 7, 8 by projection", "receipt": "certs/S-m5-lower-6.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_s_m5_rank5_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/s5_rank5/batch_manifest.json", "recomputed": 3, "compute_hours": 1700.0, "hardware": "Perlmutter CPU nodes (AMD EPYC 7763, 128 workers per node): the level-3 census in four interactive allocations on 2026-10-23 (jobs 60160192, 60160573, 60170484, 60171488; about 12 node-hours for the kernel-2 pass, 4,096 chunks, 442,623,432 prefixes, 54,157,309,763 candidates decided modulo two primes), the level-5 kappa = 0 lifts (128 chunks, minutes) and the kappa = 1 family brute force (35 bases x 243 ranges, about 2 node-hours); the other stages on an Apple silicon laptop", "note": "Stored outputs: the census (4,096 chunks of 3 or 4 pivot pairs: pairs, covers, prefixes skipped because the third letter lies in span(t, u, a) mod P1, counters), the level-5 kappa = 0 lifts (128 chunks over the 2,574 bases of results/b4_reps_v2.json), and the kappa = 1 family brute force (35 files, 243 first-option ranges each). The certificate verifies every stored output by hash and recomputes in full: letters, symmetry group, pivot pairs, the rank-4 census and its closure (the 2,160 four-term decompositions of |S>^3), the premises chi(S^3) >= 4 and chi(S^5) >= 5 exactly (a decomposition with four or fewer terms fails the run), Theorem F.3 exactly over the three representatives of |S>^4 and the complete four-qutrit letter table, the closure of the stored covers (2,013,120 in 154 orbits, representatives confirmed over Z[omega]), the P2 recheck of every one-prime skip, every level 3 to 4 lift, the 9,936 four-term decompositions of |S>^4, the 756 product-pattern completions, the span scan of all 7,439,040 four-qutrit letters, and the assembly of the 2,609 level-4 bases, then checks that the stored level-5 results cover every base with nothing found. Whole work units re-run from the seed (recomputed = 3): one census chunk with stored covers, re-enumerated with fresh functionals and compared cover for cover and skip for skip, and two kappa = 0 lift chunks; on top, three 100-prefix slices, 120 further bases, and 4 of the 8,505 family ranges. Every modular decision is exact by Hadamard's bound (minors of norm at most 6^6 against P of order 2e9). Completeness rests on the stored outputs and the committed code in research/s5_rank5, which regenerates any unit; its README has the full account.", "total": 4259 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 1800.0, "wall_clock_hours": 10.0, "runs": 2, "hardware": "Perlmutter CPU nodes (AMD EPYC 7763) for the census (two passes: kernel 1 abandoned after 1,491 chunks when its one-prime dependency screen was replaced by the two-prime decision, kernel 2 complete), the level-5 lifts and the family brute force; Apple silicon laptop (loaded, load average 70 to 100) for the controls and the other stages", "llm": [ { "model": "claude-fable-5-1", "role": "designed, wrote and ran the exclusion, its controls and this certificate" } ] } }, { "slug": "S-m5-upper-8", "file": "bounds/S-m5-upper-8.json", "orbit": "S", "m": 5, "direction": "upper", "rank": 8, "tier": "lean", "ok": true, "date": "2026-09-18", "author": "this repository", "reference": "product of board witnesses", "method": "tensor product of verified lower-m witnesses", "pull_request": 37, "merge_commit": "8123be156aa8ee0394af17b6cc170fdbff894af3", "merge_date": "2026-09-18", "added_commit": "be6917e6b0b390196a355d6051beb3197ef043d7", "added_date": "2026-09-18", "added_subject": "Fill the S and BK T-type cells at m=5, both directions", "receipt": "certs/S-m5-upper-8.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.StrangeM5StabRank", "lean_theorem": "strange_m5_stabRankP_le_eight", "lean_receipt": "certs/lean-LeanProofs-StrangeM5StabRank.json", "lean_receipt_ok": true, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop" } }, { "slug": "S-m6-lower-5", "file": "bounds/S-m6-lower-5.json", "orbit": "S", "m": 6, "direction": "lower", "rank": 5, "tier": "reproduced", "ok": true, "date": "2026-09-20", "author": "this repository", "reference": "stabrank verify_challenge", "method": "projection monotonicity applied to the slice-and-lift bound at m=5", "pull_request": 61, "merge_commit": "fec578fb6ad236de4564d49145a619b4924bd963", "merge_date": "2026-09-20", "added_commit": "801680d49c63f74d82974b5bab3f9b566965b959", "added_date": "2026-09-20", "added_subject": "Lower bounds for the five cells that had none", "receipt": "certs/S-m6-lower-5.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_s_m5_lift.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.05, "wall_clock_hours": 0.04, "runs": 1, "hardware": "the m=5 certificate, four cores" } }, { "slug": "S-m6-lower-6", "file": "bounds/S-m6-lower-6.json", "orbit": "S", "m": 6, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-10-23", "author": "Vincent Russo", "reference": "stabrank-research, round 33 (attacks/round33-strange-rank5)", "method": "recursive slice-and-lift over non-minimal covers: every five-term decomposition of |S>^5 is all full, hence a lift of a five-term decomposition of |S>^4 with nonzero coefficients; these are lifts of five-covers of |S>^3 (exact census) or completions of its four-term decompositions; no level-4 base lifts", "pull_request": 187, "merge_commit": "b0cc69b9e71e0df1a170c7abbf0ce8e6858b8310", "merge_date": "2026-10-23", "added_commit": "b42f73cccc6ddc360166b9db24de892c624ee2a3", "added_date": "2026-10-23", "added_subject": "Strange state: chi(S^5) >= 6 by a complete recursive slice-and-lift over non-minimal covers (attested), carried to m = 6, 7, 8 by projection", "receipt": "certs/S-m6-lower-6.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_s_m5_rank5_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/s5_rank5/batch_manifest.json", "recomputed": 3, "compute_hours": 1700.0, "hardware": "Perlmutter CPU nodes (AMD EPYC 7763, 128 workers per node): the level-3 census in four interactive allocations on 2026-10-23 (jobs 60160192, 60160573, 60170484, 60171488; about 12 node-hours for the kernel-2 pass, 4,096 chunks, 442,623,432 prefixes, 54,157,309,763 candidates decided modulo two primes), the level-5 kappa = 0 lifts (128 chunks, minutes) and the kappa = 1 family brute force (35 bases x 243 ranges, about 2 node-hours); the other stages on an Apple silicon laptop", "note": "Stored outputs: the census (4,096 chunks of 3 or 4 pivot pairs: pairs, covers, prefixes skipped because the third letter lies in span(t, u, a) mod P1, counters), the level-5 kappa = 0 lifts (128 chunks over the 2,574 bases of results/b4_reps_v2.json), and the kappa = 1 family brute force (35 files, 243 first-option ranges each). The certificate verifies every stored output by hash and recomputes in full: letters, symmetry group, pivot pairs, the rank-4 census and its closure (the 2,160 four-term decompositions of |S>^3), the premises chi(S^3) >= 4 and chi(S^5) >= 5 exactly (a decomposition with four or fewer terms fails the run), Theorem F.3 exactly over the three representatives of |S>^4 and the complete four-qutrit letter table, the closure of the stored covers (2,013,120 in 154 orbits, representatives confirmed over Z[omega]), the P2 recheck of every one-prime skip, every level 3 to 4 lift, the 9,936 four-term decompositions of |S>^4, the 756 product-pattern completions, the span scan of all 7,439,040 four-qutrit letters, and the assembly of the 2,609 level-4 bases, then checks that the stored level-5 results cover every base with nothing found. Whole work units re-run from the seed (recomputed = 3): one census chunk with stored covers, re-enumerated with fresh functionals and compared cover for cover and skip for skip, and two kappa = 0 lift chunks; on top, three 100-prefix slices, 120 further bases, and 4 of the 8,505 family ranges. Every modular decision is exact by Hadamard's bound (minors of norm at most 6^6 against P of order 2e9). Completeness rests on the stored outputs and the committed code in research/s5_rank5, which regenerates any unit; its README has the full account.", "total": 4259 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 1800.0, "wall_clock_hours": 10.0, "runs": 2, "hardware": "Perlmutter CPU nodes (AMD EPYC 7763) for the census (two passes: kernel 1 abandoned after 1,491 chunks when its one-prime dependency screen was replaced by the two-prime decision, kernel 2 complete), the level-5 lifts and the family brute force; Apple silicon laptop (loaded, load average 70 to 100) for the controls and the other stages", "llm": [ { "model": "claude-fable-5-1", "role": "designed, wrote and ran the exclusion, its controls and this certificate" } ] } }, { "slug": "S-m6-upper-8", "file": "bounds/S-m6-upper-8.json", "orbit": "S", "m": 6, "direction": "upper", "rank": 8, "tier": "lean", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": "certs/S-m6-upper-8.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.TensorStabRank", "lean_theorem": "strange_m6_stabRank_le_eight", "lean_receipt": "certs/lean-LeanProofs-TensorStabRank.json", "lean_receipt_ok": true, "compute": null }, { "slug": "S-m7-lower-5", "file": "bounds/S-m7-lower-5.json", "orbit": "S", "m": 7, "direction": "lower", "rank": 5, "tier": "reproduced", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank verify_challenge", "method": "projection monotonicity applied to the slice-and-lift bound at m=5", "pull_request": 177, "merge_commit": "2fffdf2d28dafba398e4162820f9df00b1eefefb", "merge_date": "2026-10-21", "added_commit": "042d19b47e51cc5cf09acaac897bce3b67dc4eb1", "added_date": "2026-10-21", "added_subject": "Carry the S lower bound to m = 7 and 8 by projection monotonicity", "receipt": "certs/S-m7-lower-5.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_s_m5_lift.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=5 certificate, which this cell re-runs" } }, { "slug": "S-m7-lower-6", "file": "bounds/S-m7-lower-6.json", "orbit": "S", "m": 7, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-10-23", "author": "Vincent Russo", "reference": "stabrank-research, round 33 (attacks/round33-strange-rank5)", "method": "recursive slice-and-lift over non-minimal covers: every five-term decomposition of |S>^5 is all full, hence a lift of a five-term decomposition of |S>^4 with nonzero coefficients; these are lifts of five-covers of |S>^3 (exact census) or completions of its four-term decompositions; no level-4 base lifts", "pull_request": 187, "merge_commit": "b0cc69b9e71e0df1a170c7abbf0ce8e6858b8310", "merge_date": "2026-10-23", "added_commit": "b42f73cccc6ddc360166b9db24de892c624ee2a3", "added_date": "2026-10-23", "added_subject": "Strange state: chi(S^5) >= 6 by a complete recursive slice-and-lift over non-minimal covers (attested), carried to m = 6, 7, 8 by projection", "receipt": "certs/S-m7-lower-6.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_s_m5_rank5_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/s5_rank5/batch_manifest.json", "recomputed": 3, "compute_hours": 1700.0, "hardware": "Perlmutter CPU nodes (AMD EPYC 7763, 128 workers per node): the level-3 census in four interactive allocations on 2026-10-23 (jobs 60160192, 60160573, 60170484, 60171488; about 12 node-hours for the kernel-2 pass, 4,096 chunks, 442,623,432 prefixes, 54,157,309,763 candidates decided modulo two primes), the level-5 kappa = 0 lifts (128 chunks, minutes) and the kappa = 1 family brute force (35 bases x 243 ranges, about 2 node-hours); the other stages on an Apple silicon laptop", "note": "Stored outputs: the census (4,096 chunks of 3 or 4 pivot pairs: pairs, covers, prefixes skipped because the third letter lies in span(t, u, a) mod P1, counters), the level-5 kappa = 0 lifts (128 chunks over the 2,574 bases of results/b4_reps_v2.json), and the kappa = 1 family brute force (35 files, 243 first-option ranges each). The certificate verifies every stored output by hash and recomputes in full: letters, symmetry group, pivot pairs, the rank-4 census and its closure (the 2,160 four-term decompositions of |S>^3), the premises chi(S^3) >= 4 and chi(S^5) >= 5 exactly (a decomposition with four or fewer terms fails the run), Theorem F.3 exactly over the three representatives of |S>^4 and the complete four-qutrit letter table, the closure of the stored covers (2,013,120 in 154 orbits, representatives confirmed over Z[omega]), the P2 recheck of every one-prime skip, every level 3 to 4 lift, the 9,936 four-term decompositions of |S>^4, the 756 product-pattern completions, the span scan of all 7,439,040 four-qutrit letters, and the assembly of the 2,609 level-4 bases, then checks that the stored level-5 results cover every base with nothing found. Whole work units re-run from the seed (recomputed = 3): one census chunk with stored covers, re-enumerated with fresh functionals and compared cover for cover and skip for skip, and two kappa = 0 lift chunks; on top, three 100-prefix slices, 120 further bases, and 4 of the 8,505 family ranges. Every modular decision is exact by Hadamard's bound (minors of norm at most 6^6 against P of order 2e9). Completeness rests on the stored outputs and the committed code in research/s5_rank5, which regenerates any unit; its README has the full account.", "total": 4259 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 1800.0, "wall_clock_hours": 10.0, "runs": 2, "hardware": "Perlmutter CPU nodes (AMD EPYC 7763) for the census (two passes: kernel 1 abandoned after 1,491 chunks when its one-prime dependency screen was replaced by the two-prime decision, kernel 2 complete), the level-5 lifts and the family brute force; Apple silicon laptop (loaded, load average 70 to 100) for the controls and the other stages", "llm": [ { "model": "claude-fable-5-1", "role": "designed, wrote and ran the exclusion, its controls and this certificate" } ] } }, { "slug": "S-m7-upper-16", "file": "bounds/S-m7-upper-16.json", "orbit": "S", "m": 7, "direction": "upper", "rank": 16, "tier": "verified", "ok": true, "date": "2026-09-22", "author": "this repository", "reference": "stabrank research/constructions/product_witness.py", "method": "structured construction", "pull_request": 104, "merge_commit": "9ce1755563ec6c7baf82903aae865f48b7668a45", "merge_date": "2026-09-22", "added_commit": "d47094a8e5a3ceb61d5905589705a08f4a9d48c8", "added_date": "2026-09-22", "added_subject": "Sweep of 2026-09-22: five product and cat witnesses, T3 sector contraction, literature update", "receipt": "certs/S-m7-upper-16.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "S-m8-lower-5", "file": "bounds/S-m8-lower-5.json", "orbit": "S", "m": 8, "direction": "lower", "rank": 5, "tier": "reproduced", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank verify_challenge", "method": "projection monotonicity applied to the slice-and-lift bound at m=5", "pull_request": 177, "merge_commit": "2fffdf2d28dafba398e4162820f9df00b1eefefb", "merge_date": "2026-10-21", "added_commit": "042d19b47e51cc5cf09acaac897bce3b67dc4eb1", "added_date": "2026-10-21", "added_subject": "Carry the S lower bound to m = 7 and 8 by projection monotonicity", "receipt": "certs/S-m8-lower-5.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_s_m5_lift.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=5 certificate, which this cell re-runs" } }, { "slug": "S-m8-lower-6", "file": "bounds/S-m8-lower-6.json", "orbit": "S", "m": 8, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-10-23", "author": "Vincent Russo", "reference": "stabrank-research, round 33 (attacks/round33-strange-rank5)", "method": "recursive slice-and-lift over non-minimal covers: every five-term decomposition of |S>^5 is all full, hence a lift of a five-term decomposition of |S>^4 with nonzero coefficients; these are lifts of five-covers of |S>^3 (exact census) or completions of its four-term decompositions; no level-4 base lifts", "pull_request": 187, "merge_commit": "b0cc69b9e71e0df1a170c7abbf0ce8e6858b8310", "merge_date": "2026-10-23", "added_commit": "b42f73cccc6ddc360166b9db24de892c624ee2a3", "added_date": "2026-10-23", "added_subject": "Strange state: chi(S^5) >= 6 by a complete recursive slice-and-lift over non-minimal covers (attested), carried to m = 6, 7, 8 by projection", "receipt": "certs/S-m8-lower-6.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_s_m5_rank5_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/s5_rank5/batch_manifest.json", "recomputed": 3, "compute_hours": 1700.0, "hardware": "Perlmutter CPU nodes (AMD EPYC 7763, 128 workers per node): the level-3 census in four interactive allocations on 2026-10-23 (jobs 60160192, 60160573, 60170484, 60171488; about 12 node-hours for the kernel-2 pass, 4,096 chunks, 442,623,432 prefixes, 54,157,309,763 candidates decided modulo two primes), the level-5 kappa = 0 lifts (128 chunks, minutes) and the kappa = 1 family brute force (35 bases x 243 ranges, about 2 node-hours); the other stages on an Apple silicon laptop", "note": "Stored outputs: the census (4,096 chunks of 3 or 4 pivot pairs: pairs, covers, prefixes skipped because the third letter lies in span(t, u, a) mod P1, counters), the level-5 kappa = 0 lifts (128 chunks over the 2,574 bases of results/b4_reps_v2.json), and the kappa = 1 family brute force (35 files, 243 first-option ranges each). The certificate verifies every stored output by hash and recomputes in full: letters, symmetry group, pivot pairs, the rank-4 census and its closure (the 2,160 four-term decompositions of |S>^3), the premises chi(S^3) >= 4 and chi(S^5) >= 5 exactly (a decomposition with four or fewer terms fails the run), Theorem F.3 exactly over the three representatives of |S>^4 and the complete four-qutrit letter table, the closure of the stored covers (2,013,120 in 154 orbits, representatives confirmed over Z[omega]), the P2 recheck of every one-prime skip, every level 3 to 4 lift, the 9,936 four-term decompositions of |S>^4, the 756 product-pattern completions, the span scan of all 7,439,040 four-qutrit letters, and the assembly of the 2,609 level-4 bases, then checks that the stored level-5 results cover every base with nothing found. Whole work units re-run from the seed (recomputed = 3): one census chunk with stored covers, re-enumerated with fresh functionals and compared cover for cover and skip for skip, and two kappa = 0 lift chunks; on top, three 100-prefix slices, 120 further bases, and 4 of the 8,505 family ranges. Every modular decision is exact by Hadamard's bound (minors of norm at most 6^6 against P of order 2e9). Completeness rests on the stored outputs and the committed code in research/s5_rank5, which regenerates any unit; its README has the full account.", "total": 4259 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 1800.0, "wall_clock_hours": 10.0, "runs": 2, "hardware": "Perlmutter CPU nodes (AMD EPYC 7763) for the census (two passes: kernel 1 abandoned after 1,491 chunks when its one-prime dependency screen was replaced by the two-prime decision, kernel 2 complete), the level-5 lifts and the family brute force; Apple silicon laptop (loaded, load average 70 to 100) for the controls and the other stages", "llm": [ { "model": "claude-fable-5-1", "role": "designed, wrote and ran the exclusion, its controls and this certificate" } ] } }, { "slug": "S-m8-upper-16", "file": "bounds/S-m8-upper-16.json", "orbit": "S", "m": 8, "direction": "upper", "rank": 16, "tier": "verified", "ok": true, "date": "2026-09-22", "author": "this repository", "reference": "stabrank research/constructions/product_witness.py", "method": "structured construction", "pull_request": 104, "merge_commit": "9ce1755563ec6c7baf82903aae865f48b7668a45", "merge_date": "2026-09-22", "added_commit": "d47094a8e5a3ceb61d5905589705a08f4a9d48c8", "added_date": "2026-09-22", "added_subject": "Sweep of 2026-09-22: five product and cat witnesses, T3 sector contraction, literature update", "receipt": "certs/S-m8-upper-16.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "T3-m1-lower-3", "file": "bounds/T3-m1-lower-3.json", "orbit": "T3", "m": 1, "direction": "lower", "rank": 3, "tier": "lean", "ok": true, "date": "2026-09-16", "author": "this repository", "reference": "stabrank PR #19", "method": "exhaustion over all 66 pairs of 1-qutrit stabilizer states", "pull_request": 19, "merge_commit": "108ccb1d8afcd6a1ef3f43b954c67719849db9c7", "merge_date": "2026-09-16", "added_commit": "9c7e34e6fc813ab13e4b7ac1635972823689d157", "added_date": "2026-09-16", "added_subject": "Certify chi(|T3>) >= 3, settling chi(|T3>) = 3", "receipt": "certs/T3-m1-lower-3.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_t3m1_rank2.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.T3M1StabRank", "lean_theorem": "t3_m1_stabRank_gt_two", "lean_receipt": "certs/lean-LeanProofs-T3M1StabRank.json", "lean_receipt_ok": true, "compute": null }, { "slug": "T3-m1-upper-3", "file": "bounds/T3-m1-upper-3.json", "orbit": "T3", "m": 1, "direction": "upper", "rank": 3, "tier": "lean", "ok": true, "date": "2020-03-02", "author": "Kocia and Sarovar", "reference": "arXiv:2003.01130", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": "certs/T3-m1-upper-3.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.M1StabRank", "lean_theorem": "t3_m1_stabRank_le_three", "lean_receipt": "certs/lean-LeanProofs-M1StabRank.json", "lean_receipt_ok": true, "compute": null }, { "slug": "T3-m2-lower-3", "file": "bounds/T3-m2-lower-3.json", "orbit": "T3", "m": 2, "direction": "lower", "rank": 3, "tier": "lean", "ok": true, "date": "2026-09-07", "author": "this repository", "reference": "stabrank PR #16", "method": "Galois descent over Z[w3]; no search", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": "certs/T3-m2-lower-3.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_t3_galois.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.T3GaloisM", "lean_theorem": "t3_m2_stabRank_gt_two", "lean_receipt": "certs/lean-LeanProofs-T3GaloisM.json", "lean_receipt_ok": true, "compute": null }, { "slug": "T3-m2-upper-3", "file": "bounds/T3-m2-upper-3.json", "orbit": "T3", "m": 2, "direction": "upper", "rank": 3, "tier": "lean", "ok": true, "date": "2020-03-02", "author": "Kocia and Sarovar", "reference": "arXiv:2003.01130", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": null, "receipt_matches": null, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.T3M2StabRank", "lean_theorem": "t3_m2_stabRank_le_three", "lean_receipt": "certs/lean-LeanProofs-T3M2StabRank.json", "lean_receipt_ok": true, "compute": null }, { "slug": "T3-m3-lower-6", "file": "bounds/T3-m3-lower-6.json", "orbit": "T3", "m": 3, "direction": "lower", "rank": 6, "tier": "reproduced", "ok": true, "date": "2026-09-07", "author": "this repository", "reference": "stabrank PR #16", "method": "Galois descent to cut the search to finitely many candidate lines, then exhaustion", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "a9a34259861f9dacc20c85b18d1120b9bd8c200e", "added_date": "2026-09-12", "added_subject": "Date submissions properly and put chi(T3^3) >= 6 on the board", "receipt": "certs/T3-m3-lower-6.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_t3m3_rank6.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": null }, { "slug": "T3-m3-lower-7", "file": "bounds/T3-m3-lower-7.json", "orbit": "T3", "m": 3, "direction": "lower", "rank": 7, "tier": "verified", "ok": true, "date": "2026-09-16", "author": "this repository", "reference": "stabrank PR #41", "method": "Galois descent to Q(w3), then exhaustive coplanarity scan of six-state configurations in exact arithmetic mod two primes", "pull_request": 41, "merge_commit": "0c4c8fefb1512ca1ea78a5626c03a19e9843e310", "merge_date": "2026-09-18", "added_commit": "263a82903ad284dbb8306fd8e057f07c6e40d0b5", "added_date": "2026-09-18", "added_subject": "Certify chi(T3^3) >= 7 by exact exclusion of rank-6 configurations", "receipt": "certs/T3-m3-lower-7.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_t3m3_rank7.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.15, "wall_clock_hours": 0.04, "runs": 2, "hardware": "Apple silicon laptop, 8 workers: 99 s wall and 270 s CPU in the worktree, 135 s wall and 486 s CPU on the rebased branch; about three minutes on the 4-core CI runner" } }, { "slug": "T3-m3-lower-8", "file": "bounds/T3-m3-lower-8.json", "orbit": "T3", "m": 3, "direction": "lower", "rank": 8, "tier": "attested", "ok": true, "date": "2026-09-20", "author": "this repository", "reference": "stabrank research/t3_rank7", "method": "Galois descent to Q(w3), then exhaustive three-pivot scan of seven-state configurations in exact arithmetic, batched and attested", "pull_request": 62, "merge_commit": "f426dcd36d90e8baf5dd1f96ac2ddc35e6907941", "merge_date": "2026-09-20", "added_commit": "937e5c4b7c061f95d340bcabdb3efdf5da04707f", "added_date": "2026-09-20", "added_subject": "chi(T3^3) >= 8: the exact rank-7 exclusion, attested over 459 stored batches", "receipt": "certs/T3-m3-lower-8.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_t3m3_rank8_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/t3_rank7/batch_manifest.json", "recomputed": 2, "compute_hours": 80.1, "hardware": "Apple silicon laptop (18 cores), four batches at a time at nice 19 under a shared load; 2026-09-19 13:33 to 2026-09-20 11:33 UTC", "note": "The enumeration of every rank-7 candidate class set (1.31e13 inner steps, 1.21e9 class sets, all decided exactly) lives in the 459 stored batch outputs; the certificate verifies their hashes, geometry and totals and re-runs two of them from scratch, so completeness rests on the stored outputs and on the committed runner that regenerates any batch.", "total": 459 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 468.7, "wall_clock_hours": 115.8, "runs": 4, "hardware": "Apple silicon laptop, four loop.py instances at nice 19 over the 459-batch partition, 21 ns per inner step averaged (80.1 CPU-h, 22 h wall); independent exclusion of research/t3_rank7/independent: RunPod Xeon Gold 6342 pod, 6 workers at nice 10 under a shared 7.65-core quota, 37 ns per step per worker (378.5 CPU-h over 92.9 h wall in two sessions), plus the laptop supplement of the skipped third pivots, 14 workers (10.1 CPU-h, 0.75 h wall)" } }, { "slug": "T3-m3-upper-8", "file": "bounds/T3-m3-upper-8.json", "orbit": "T3", "m": 3, "direction": "upper", "rank": 8, "tier": "lean", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": "certs/T3-m3-upper-8.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.T3M3StabRank", "lean_theorem": "t3_m3_stabRankP_le_eight", "lean_receipt": "certs/lean-LeanProofs-T3M3StabRank.json", "lean_receipt_ok": true, "compute": null }, { "slug": "T3-m4-lower-6", "file": "bounds/T3-m4-lower-6.json", "orbit": "T3", "m": 4, "direction": "lower", "rank": 6, "tier": "reproduced", "ok": true, "date": "2026-09-16", "author": "this repository", "reference": "stabrank cert_t3m3_rank6.py", "method": "projection monotonicity applied to the certified chi(T3^3) >= 6", "pull_request": 24, "merge_commit": "7e72a78cefefa660acca809d2c7275424fb32258", "merge_date": "2026-09-17", "added_commit": "19fd51cfa2a46b7c8c818baefa784842d97b07d7", "added_date": "2026-09-16", "added_subject": "Certify nine lower bounds: five cells settled, T3 at m=4 bounded for the first time", "receipt": "certs/T3-m4-lower-6.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_t3_m4_from_m3.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.2, "wall_clock_hours": 0.05, "runs": 1, "hardware": "Apple silicon laptop, 6 worker processes" } }, { "slug": "T3-m4-lower-8", "file": "bounds/T3-m4-lower-8.json", "orbit": "T3", "m": 4, "direction": "lower", "rank": 8, "tier": "attested", "ok": true, "date": "2026-09-20", "author": "this repository", "reference": "stabrank research/t3_rank7", "method": "projection monotonicity applied to the attested exact rank-7 exclusion at m=3", "pull_request": 76, "merge_commit": "719ffdd854943e3c4f5baab490b66e65e7d83969", "merge_date": "2026-09-20", "added_commit": "4e0e378c86cc4a933a1dec59639c7283abde5e0c", "added_date": "2026-09-20", "added_subject": "chi(T3^4) >= 8 by projection from the attested m=3 value", "receipt": "certs/T3-m4-lower-8.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_t3m3_rank8_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/t3_rank7/batch_manifest.json", "recomputed": 2, "compute_hours": 80.1, "hardware": "Apple silicon laptop (18 cores), four batches at a time at nice 19 under a shared load; 2026-09-19 13:33 to 2026-09-20 11:33 UTC", "note": "The enumeration of every rank-7 candidate class set (1.31e13 inner steps, 1.21e9 class sets, all decided exactly) lives in the 459 stored batch outputs; the certificate verifies their hashes, geometry and totals and re-runs two of them from scratch, so completeness rests on the stored outputs and on the committed runner that regenerates any batch.", "total": 459 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=3 certificate, which this cell re-runs" } }, { "slug": "T3-m4-upper-9", "file": "bounds/T3-m4-upper-9.json", "orbit": "T3", "m": 4, "direction": "upper", "rank": 9, "tier": "lean", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": "certs/T3-m4-upper-9.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.T3M4StabRank", "lean_theorem": "t3_m4_stabRankP_le_nine", "lean_receipt": "certs/lean-LeanProofs-T3M4StabRank.json", "lean_receipt_ok": true, "compute": null }, { "slug": "T3-m5-lower-6", "file": "bounds/T3-m5-lower-6.json", "orbit": "T3", "m": 5, "direction": "lower", "rank": 6, "tier": "reproduced", "ok": true, "date": "2026-09-18", "author": "this repository", "reference": "stabrank cert_t3m3_rank6.py", "method": "projection monotonicity applied twice to the certified chi(T3^3) >= 6", "pull_request": 30, "merge_commit": "e9d39c1ab569d42d757894947c6e6a895d7edf6b", "merge_date": "2026-09-18", "added_commit": "e0f69b94e43aa5b8107e4aaeb3e0da79ab19a29e", "added_date": "2026-09-18", "added_subject": "chi(|T3>^5) >= 6 by projection monotonicity from the certified m=3 bound", "receipt": "certs/T3-m5-lower-6.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_t3_m5_from_m3.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.15, "wall_clock_hours": 0.03, "runs": 1, "hardware": "Apple silicon laptop, 6 worker processes" } }, { "slug": "T3-m5-lower-8", "file": "bounds/T3-m5-lower-8.json", "orbit": "T3", "m": 5, "direction": "lower", "rank": 8, "tier": "attested", "ok": true, "date": "2026-09-20", "author": "this repository", "reference": "stabrank research/t3_rank7", "method": "projection monotonicity applied to the attested exact rank-7 exclusion at m=3", "pull_request": 77, "merge_commit": "54bddb896e5c9894c7aa0ec2ff5a266984efc618", "merge_date": "2026-09-20", "added_commit": "9b73208a0c702474c06ad591f00a59a77cdfaa4a", "added_date": "2026-09-20", "added_subject": "chi(T3^5) >= 8 by projection from the attested m=3 value", "receipt": "certs/T3-m5-lower-8.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_t3m3_rank8_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/t3_rank7/batch_manifest.json", "recomputed": 2, "compute_hours": 80.1, "hardware": "Apple silicon laptop (18 cores), four batches at a time at nice 19 under a shared load; 2026-09-19 13:33 to 2026-09-20 11:33 UTC", "note": "The enumeration of every rank-7 candidate class set (1.31e13 inner steps, 1.21e9 class sets, all decided exactly) lives in the 459 stored batch outputs; the certificate verifies their hashes, geometry and totals and re-runs two of them from scratch, so completeness rests on the stored outputs and on the committed runner that regenerates any batch.", "total": 459 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=3 certificate, which this cell re-runs" } }, { "slug": "T3-m5-upper-18", "file": "bounds/T3-m5-upper-18.json", "orbit": "T3", "m": 5, "direction": "upper", "rank": 18, "tier": "lean", "ok": true, "date": "2026-09-17", "author": "this repository", "reference": "stabrank sector-state search", "method": "Z^5 sector (qutrit cat-state) decomposition: each of the three sector projections of |T3>^5 is a 4-qutrit carry state, annealed to rank 6 on its code space and lifted; exact coefficients over Q(w9)", "pull_request": 28, "merge_commit": "7218b42197fa8fa2a9bce61449e833ddc41067b7", "merge_date": "2026-09-17", "added_commit": "45e4728041192cdea9ffba44ff3274ae15df2324", "added_date": "2026-09-17", "added_subject": "chi(|T3>^5) <= 18 by a qutrit cat-state decomposition", "receipt": "certs/T3-m5-upper-18.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.T3M5StabRank", "lean_theorem": "t3_m5_stabRankP_le_eighteen", "lean_receipt": "certs/lean-LeanProofs-T3M5StabRank.json", "lean_receipt_ok": true, "compute": { "cpu_hours": 0.6, "wall_clock_hours": 0.5, "runs": 8, "hardware": "Apple silicon laptop under heavy load from other jobs, 8 annealing chains per run", "llm": [ { "model": "claude-fable-5-1", "role": "designed the sector decomposition and drove the search" } ] } }, { "slug": "T3-m6-lower-8", "file": "bounds/T3-m6-lower-8.json", "orbit": "T3", "m": 6, "direction": "lower", "rank": 8, "tier": "attested", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank research/t3_rank7", "method": "projection monotonicity applied to the attested exact rank-7 exclusion at m=3", "pull_request": 181, "merge_commit": "08e62371708443044beaf7765e8e303991a4ee43", "merge_date": "2026-10-21", "added_commit": "0a64f225e117af8ac19dfff8c1f5a8c32e3c582d", "added_date": "2026-10-21", "added_subject": "Carry the T3 lower bound to m = 6 by projection monotonicity", "receipt": "certs/T3-m6-lower-8.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_t3m3_rank8_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/t3_rank7/batch_manifest.json", "recomputed": 2, "compute_hours": 80.1, "hardware": "Apple silicon laptop (18 cores), four batches at a time at nice 19 under a shared load; 2026-09-19 13:33 to 2026-09-20 11:33 UTC", "note": "The enumeration of every rank-7 candidate class set (1.31e13 inner steps, 1.21e9 class sets, all decided exactly) lives in the 459 stored batch outputs; the certificate verifies their hashes, geometry and totals and re-runs two of them from scratch, so completeness rests on the stored outputs and on the committed runner that regenerates any batch.", "total": 459 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=3 certificate, which this cell re-runs" } }, { "slug": "T3-m6-upper-27", "file": "bounds/T3-m6-upper-27.json", "orbit": "T3", "m": 6, "direction": "upper", "rank": 27, "tier": "verified", "ok": true, "date": "2026-09-23", "author": "this repository", "reference": "stabrank research/constructions/product_witness.py", "method": "structured construction", "pull_request": 115, "merge_commit": "2ce2188bcde0855200b915c35bedefc598af266a", "merge_date": "2026-09-23", "added_commit": "bd2b13d4cf153ba9321cfa2faf4143e5c8472ba3", "added_date": "2026-09-23", "added_subject": "Sweep of 2026-09-23: T5 and qutrit product witnesses, a T5 m=2 rank-7 search, literature update", "receipt": "certs/T3-m6-upper-27.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "T5-m1-lower-3", "file": "bounds/T5-m1-lower-3.json", "orbit": "T5", "m": 1, "direction": "lower", "rank": 3, "tier": "lean", "ok": true, "date": "2026-09-21", "author": "this repository", "reference": "stabrank verify_challenge", "method": "exact: every 3 x 3 minor of [s | t | psi] over all 435 pairs of the 30 single-ququint stabilizer states, decided in Z[w_5]", "pull_request": 84, "merge_commit": "b45e9f8894c60b8a907611865eaa0f5230b38757", "merge_date": "2026-09-21", "added_commit": "df562d18db99db759bcff4d509cfd9691b0bd471", "added_date": "2026-09-21", "added_subject": "Make the ququint T-type state T5 a board orbit with its first four cells", "receipt": "certs/T5-m1-lower-3.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_t5_m1_rank2.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.T5M1StabRank", "lean_theorem": "t5_m1_stabRankP_gt_two", "lean_receipt": "certs/lean-LeanProofs-T5M1StabRank.json", "lean_receipt_ok": true, "compute": null }, { "slug": "T5-m1-upper-3", "file": "bounds/T5-m1-upper-3.json", "orbit": "T5", "m": 1, "direction": "upper", "rank": 3, "tier": "lean", "ok": true, "date": "2026-09-20", "author": "this repository", "reference": "stabrank docs/notes/new_orbits_design.md", "method": "pivot search over the 30 single-ququint stabilizer states, then exact refit with fit_coeffs.fit", "pull_request": 84, "merge_commit": "b45e9f8894c60b8a907611865eaa0f5230b38757", "merge_date": "2026-09-21", "added_commit": "df562d18db99db759bcff4d509cfd9691b0bd471", "added_date": "2026-09-21", "added_subject": "Make the ququint T-type state T5 a board orbit with its first four cells", "receipt": "certs/T5-m1-upper-3.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.T5M1StabRank", "lean_theorem": "t5_m1_stabRankP_le_three", "lean_receipt": "certs/lean-LeanProofs-T5M1StabRank.json", "lean_receipt_ok": true, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core" } }, { "slug": "T5-m2-lower-5", "file": "bounds/T5-m2-lower-5.json", "orbit": "T5", "m": 2, "direction": "lower", "rank": 5, "tier": "reproduced", "ok": true, "date": "2026-09-21", "author": "this repository", "reference": "stabrank docs/notes/new_orbits_design.md", "method": "rank-3 exclusion by pivot-and-quotient from 66 symmetry representatives, then rank-4 exclusion by the pivot-pair search of slice_lift.py from 98 representatives, over the 3,900 two-ququint stabilizer states", "pull_request": 84, "merge_commit": "b45e9f8894c60b8a907611865eaa0f5230b38757", "merge_date": "2026-09-21", "added_commit": "df562d18db99db759bcff4d509cfd9691b0bd471", "added_date": "2026-09-21", "added_subject": "Make the ququint T-type state T5 a board orbit with its first four cells", "receipt": "certs/T5-m2-lower-5.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_t5_m2_rank4.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.04, "wall_clock_hours": 0.04, "runs": 2, "hardware": "Apple silicon laptop, one core: 82 s for the first rank-4 run, 51 s for the certificate" } }, { "slug": "T5-m2-upper-5", "file": "bounds/T5-m2-upper-5.json", "orbit": "T5", "m": 2, "direction": "upper", "rank": 5, "tier": "lean", "ok": true, "date": "2026-09-24", "author": "this repository", "reference": "stabrank docs/notes/t5q_m2_rank5_exclusion.md", "method": "direct census of the 5-sets of two-ququint stabilizer states whose span contains |T5>^2 (compiled 5-cover kernel, one set per orbit of the unitary symmetry group), then exact refit", "pull_request": 138, "merge_commit": "70fffa011385518adc4095cd608a1930d8271863", "merge_date": "2026-09-24", "added_commit": "adc82188a67452918eb9392d57d5b8fe11b61a68", "added_date": "2026-09-24", "added_subject": "chi(T5^2) = 5: the rank-5 witness of |T5>^2 and its products at m = 3 and 4", "receipt": null, "receipt_matches": null, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.T5M2StabRank", "lean_theorem": "t5_m2_stabRankP_le_five", "lean_receipt": "certs/lean-LeanProofs-T5M2StabRank.json", "lean_receipt_ok": true, "compute": { "cpu_hours": 13.4, "wall_clock_hours": 1.06, "runs": 74, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host, fifteen batches in parallel at nice 19 (2026-09-24 12:32 to 13:36 UTC); about 0.3 laptop CPU-hours of controls before it" } }, { "slug": "T5-m2-upper-8", "file": "bounds/T5-m2-upper-8.json", "orbit": "T5", "m": 2, "direction": "upper", "rank": 8, "tier": "lean", "ok": true, "date": "2026-09-21", "author": "this repository", "reference": "stabrank autoresearch/run.py", "method": "simulated annealing at rank 8 (4 chains, 8000 iterations per temperature, cooling 0.995), then exact refit", "pull_request": 84, "merge_commit": "b45e9f8894c60b8a907611865eaa0f5230b38757", "merge_date": "2026-09-21", "added_commit": "df562d18db99db759bcff4d509cfd9691b0bd471", "added_date": "2026-09-21", "added_subject": "Make the ququint T-type state T5 a board orbit with its first four cells", "receipt": "certs/T5-m2-upper-8.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.T5M2StabRank", "lean_theorem": "t5_m2_stabRankP_le_eight", "lean_receipt": "certs/lean-LeanProofs-T5M2StabRank.json", "lean_receipt_ok": true, "compute": { "cpu_hours": 0.1513, "wall_clock_hours": 0.0479, "runs": 2, "hardware": "arm64 Darwin, 18 cores" } }, { "slug": "T5-m3-lower-5", "file": "bounds/T5-m3-lower-5.json", "orbit": "T5", "m": 3, "direction": "lower", "rank": 5, "tier": "reproduced", "ok": true, "date": "2026-09-24", "author": "this repository", "reference": "stabrank verify_challenge", "method": "projection monotonicity applied to the exact rank-4 exclusion at m=2", "pull_request": 138, "merge_commit": "70fffa011385518adc4095cd608a1930d8271863", "merge_date": "2026-09-24", "added_commit": "21ac4ab44e2fb5178528e0b66c4800581af82753", "added_date": "2026-09-24", "added_subject": "T5 m = 3 and 4: lower bound 5 by projection from the rank-4 exclusion at m = 2", "receipt": "certs/T5-m3-lower-5.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_t5_m2_rank4.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=2 certificate, which this cell re-runs" } }, { "slug": "T5-m3-lower-6", "file": "bounds/T5-m3-lower-6.json", "orbit": "T5", "m": 3, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-10-02", "author": "this repository", "reference": "stabrank docs/notes/t5_m3_lift_design.md", "method": "slice-and-lift at exact rank: the census listing of the rank-5 decompositions of |T5>^2 (one set, the five Z(x)Z eigensectors) lifted along a third ququint by an exact pattern search over Q(zeta_5); no pattern vector is a stabilizer state", "pull_request": 162, "merge_commit": "790bf24279e4118619c4ed1144e053491648404e", "merge_date": "2026-10-15", "added_commit": "f325934dbef9f2a54bdc8e25ca33cfd57245590c", "added_date": "2026-10-01", "added_subject": "chi(T5^3) >= 6 at the attested tier: the pod run, the census re-run, and the bounds", "receipt": "certs/T5-m3-lower-6.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_t5_m3_lift_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/t5q_m2_rank5/batch_manifest.json", "recomputed": 2, "compute_hours": 13.4, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host, fifteen batches in parallel at nice 19, 2026-09-24 12:32 to 13:36 UTC (the rank-5 census of |T5>^2, research/t5q_m2_rank5 at commit 2b751cb)", "note": "The listing of every 5-set of two-ququint stabilizer states whose span contains |T5>^2, one per orbit of the unitary symmetry group, lives in the stored batch outputs under research/t5q_m2_rank5/results/ (74 batches, 155,422 pivot-partner units, every unit run, 0 undecided, one hit: the five Z(x)Z eigensectors, a set fixed by the group). The enumeration was not re-run under the budget. The certificate re-enumerates the plan, re-runs the exact k = 1..4 censuses, verifies the hashes and geometry of every output, re-decides the stored hit, fails on any undecided unit, re-runs two batches from scratch (seed 20261001: batches 12 and 47), and then runs the exact lift decision of research/t5_m3_lift/lift.py on the listed set. Completeness rests on the stored outputs and on research/t5q_m2_rank5/batch.py, which regenerates any batch (batch.py K), under the modular assumption every kernel census of the project makes: a member whose image is nonzero over Q(zeta_5) is nonzero modulo 65521. An independent re-run of all 74 batches on 2026-10-02 (research/t5_m3_lift/results/pod/census/) reproduced every deterministic hash; it is recorded in provenance.compute and does not change the tier.", "total": 74 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 28.9, "wall_clock_hours": 2.9, "runs": 2, "hardware": "Two census runs and the lift chain. (1) The rank-5 census of |T5>^2, 2026-09-24 12:32 to 13:36 UTC: 13.4 CPU-hours on a RunPod pod, 16 vCPU AMD EPYC 4564P on a shared host, fifteen batches at nice 19, commit 2b751cb, Python 3.12.14, numpy 2.3.5 (the attested enumeration). (2) The same 74 batches again, 2026-10-02 01:43 to 02:32 UTC: 14.5 CPU-hours (14.57 kernel hours, 1.15e-7 s per squared member count) on a RunPod pod, 32 vCPU AMD EPYC 9655P, 20 batches at nice 19, commit b894242 with the 5-cover kernel source as refactored after the first run (561c82a), built with gcc-10, Python 3.13.5, numpy 2.4.4; the deterministic hash of every one of the 74 records (units, member counts, hits with their decisions, undecided lists) equals the committed one, with the same 2,795,734,903 modular candidates and the same single hit. (3) The chain around it on the second pod, 01:30 to 03:19 UTC, about 1 CPU-hour: the census and lift controls, the batch-73 probe (404 kernel s, hash equal), the listing aggregate with its two seeded re-runs (batches 12 and 47, 591 s and 571 s, hashes equal), the lift stage (168 s with the exact k = 1..4 censuses, 0.05 s of search), and the certificate under the verifier (attested, 22 minutes). Laptop controls before the pod: 0.1 CPU-hours." } }, { "slug": "T5-m3-upper-15", "file": "bounds/T5-m3-upper-15.json", "orbit": "T5", "m": 3, "direction": "upper", "rank": 15, "tier": "lean", "ok": true, "date": "2026-09-24", "author": "this repository", "reference": "stabrank research/constructions/product_witness.py", "method": "structured construction", "pull_request": 138, "merge_commit": "70fffa011385518adc4095cd608a1930d8271863", "merge_date": "2026-09-24", "added_commit": "adc82188a67452918eb9392d57d5b8fe11b61a68", "added_date": "2026-09-24", "added_subject": "chi(T5^2) = 5: the rank-5 witness of |T5>^2 and its products at m = 3 and 4", "receipt": null, "receipt_matches": null, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.T5M3StabRank", "lean_theorem": "t5_m3_stabRankP_le_fifteen", "lean_receipt": "certs/lean-LeanProofs-T5M3StabRank.json", "lean_receipt_ok": true, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "T5-m4-lower-5", "file": "bounds/T5-m4-lower-5.json", "orbit": "T5", "m": 4, "direction": "lower", "rank": 5, "tier": "reproduced", "ok": true, "date": "2026-09-24", "author": "this repository", "reference": "stabrank verify_challenge", "method": "projection monotonicity applied to the exact rank-4 exclusion at m=2", "pull_request": 138, "merge_commit": "70fffa011385518adc4095cd608a1930d8271863", "merge_date": "2026-09-24", "added_commit": "21ac4ab44e2fb5178528e0b66c4800581af82753", "added_date": "2026-09-24", "added_subject": "T5 m = 3 and 4: lower bound 5 by projection from the rank-4 exclusion at m = 2", "receipt": "certs/T5-m4-lower-5.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_t5_m2_rank4.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=2 certificate, which this cell re-runs" } }, { "slug": "T5-m4-lower-6", "file": "bounds/T5-m4-lower-6.json", "orbit": "T5", "m": 4, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-10-02", "author": "this repository", "reference": "stabrank research/t5_m3_lift", "method": "projection monotonicity applied to the attested slice-and-lift exclusion of rank 5 at m=3", "pull_request": 162, "merge_commit": "790bf24279e4118619c4ed1144e053491648404e", "merge_date": "2026-10-15", "added_commit": "f325934dbef9f2a54bdc8e25ca33cfd57245590c", "added_date": "2026-10-01", "added_subject": "chi(T5^3) >= 6 at the attested tier: the pod run, the census re-run, and the bounds", "receipt": "certs/T5-m4-lower-6.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_t5_m3_lift_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/t5q_m2_rank5/batch_manifest.json", "recomputed": 2, "compute_hours": 13.4, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host, fifteen batches in parallel at nice 19, 2026-09-24 12:32 to 13:36 UTC (the rank-5 census of |T5>^2, research/t5q_m2_rank5 at commit 2b751cb)", "note": "The listing of every 5-set of two-ququint stabilizer states whose span contains |T5>^2, one per orbit of the unitary symmetry group, lives in the stored batch outputs under research/t5q_m2_rank5/results/ (74 batches, 155,422 pivot-partner units, every unit run, 0 undecided, one hit: the five Z(x)Z eigensectors, a set fixed by the group). The enumeration was not re-run under the budget. The certificate re-enumerates the plan, re-runs the exact k = 1..4 censuses, verifies the hashes and geometry of every output, re-decides the stored hit, fails on any undecided unit, re-runs two batches from scratch (seed 20261001: batches 12 and 47), and then runs the exact lift decision of research/t5_m3_lift/lift.py on the listed set. Completeness rests on the stored outputs and on research/t5q_m2_rank5/batch.py, which regenerates any batch (batch.py K), under the modular assumption every kernel census of the project makes: a member whose image is nonzero over Q(zeta_5) is nonzero modulo 65521. An independent re-run of all 74 batches on 2026-10-02 (research/t5_m3_lift/results/pod/census/) reproduced every deterministic hash; it is recorded in provenance.compute and does not change the tier.", "total": 74 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=3 certificate, which this cell re-runs" } }, { "slug": "T5-m4-upper-25", "file": "bounds/T5-m4-upper-25.json", "orbit": "T5", "m": 4, "direction": "upper", "rank": 25, "tier": "lean", "ok": true, "date": "2026-09-24", "author": "this repository", "reference": "stabrank research/constructions/product_witness.py", "method": "structured construction", "pull_request": 138, "merge_commit": "70fffa011385518adc4095cd608a1930d8271863", "merge_date": "2026-09-24", "added_commit": "adc82188a67452918eb9392d57d5b8fe11b61a68", "added_date": "2026-09-24", "added_subject": "chi(T5^2) = 5: the rank-5 witness of |T5>^2 and its products at m = 3 and 4", "receipt": null, "receipt_matches": null, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.T5M4StabRank", "lean_theorem": "t5_m4_stabRankP_le_twentyfive", "lean_receipt": "certs/lean-LeanProofs-T5M4StabRank.json", "lean_receipt_ok": true, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "T5-m5-lower-6", "file": "bounds/T5-m5-lower-6.json", "orbit": "T5", "m": 5, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank research/t5_m3_lift", "method": "projection monotonicity applied to the attested lift bound at m=3", "pull_request": 182, "merge_commit": "c8156efbd94fb0c703676d8de77682a8f6207464", "merge_date": "2026-10-21", "added_commit": "0c278d2955dbfcaac679a51a3e7db9dd9e5e29b1", "added_date": "2026-10-21", "added_subject": "Carry the T5 lower bound to m = 5 by projection monotonicity", "receipt": "certs/T5-m5-lower-6.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_t5_m3_lift_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/t5q_m2_rank5/batch_manifest.json", "recomputed": 2, "compute_hours": 13.4, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host, fifteen batches in parallel at nice 19, 2026-09-24 12:32 to 13:36 UTC (the rank-5 census of |T5>^2, research/t5q_m2_rank5 at commit 2b751cb)", "note": "The listing of every 5-set of two-ququint stabilizer states whose span contains |T5>^2, one per orbit of the unitary symmetry group, lives in the stored batch outputs under research/t5q_m2_rank5/results/ (74 batches, 155,422 pivot-partner units, every unit run, 0 undecided, one hit: the five Z(x)Z eigensectors, a set fixed by the group). The enumeration was not re-run under the budget. The certificate re-enumerates the plan, re-runs the exact k = 1..4 censuses, verifies the hashes and geometry of every output, re-decides the stored hit, fails on any undecided unit, re-runs two batches from scratch (seed 20261001: batches 12 and 47), and then runs the exact lift decision of research/t5_m3_lift/lift.py on the listed set. Completeness rests on the stored outputs and on research/t5q_m2_rank5/batch.py, which regenerates any batch (batch.py K), under the modular assumption every kernel census of the project makes: a member whose image is nonzero over Q(zeta_5) is nonzero modulo 65521. An independent re-run of all 74 batches on 2026-10-02 (research/t5_m3_lift/results/pod/census/) reproduced every deterministic hash; it is recorded in provenance.compute and does not change the tier.", "total": 74 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=3 certificate, which this cell re-runs" } }, { "slug": "T5-m5-upper-75", "file": "bounds/T5-m5-upper-75.json", "orbit": "T5", "m": 5, "direction": "upper", "rank": 75, "tier": "verified", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank research/constructions/product_witness.py", "method": "structured construction", "pull_request": 177, "merge_commit": "2fffdf2d28dafba398e4162820f9df00b1eefefb", "merge_date": "2026-10-21", "added_commit": "5a03130789330826b73202e9c6e68e0031dff684", "added_date": "2026-10-21", "added_subject": "Add chi(T5^5) <= 75 from the product of the m = 2 and m = 3 witnesses, and drop nsimplify from product_witness.py", "receipt": "certs/T5-m5-upper-75.json", "receipt_matches": true, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "cat-m2-upper-1", "file": "bounds/cat-m2-upper-1.json", "orbit": "cat", "m": 2, "direction": "upper", "rank": 1, "tier": "verified", "ok": true, "date": "2021-06-14", "author": "Qassim, Pashayan, and Gosset", "reference": "arXiv:2106.07740", "method": "literature", "pull_request": 141, "merge_commit": "17b9c1f584f9784436d271c763fbe07ef7bf3c6c", "merge_date": "2026-09-24", "added_commit": "e84a236183ba4a9df078a6f52c71e66043e47ad9", "added_date": "2026-09-24", "added_subject": "Add the magic cat track: cat_m targets, implied H exponent, and the QPG cells", "receipt": "certs/cat-m2-upper-1.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": null }, { "slug": "cat-m3-lower-2", "file": "bounds/cat-m3-lower-2.json", "orbit": "cat", "m": 3, "direction": "lower", "rank": 2, "tier": "verified", "ok": true, "date": "2026-09-24", "author": "this repository", "reference": "stabrank verify_challenge", "method": "exact: the state is not a stabilizer state (its phase on the even-weight strings is not a Z_4 quadratic form)", "pull_request": 141, "merge_commit": "17b9c1f584f9784436d271c763fbe07ef7bf3c6c", "merge_date": "2026-09-24", "added_commit": "e84a236183ba4a9df078a6f52c71e66043e47ad9", "added_date": "2026-09-24", "added_subject": "Add the magic cat track: cat_m targets, implied H exponent, and the QPG cells", "receipt": "certs/cat-m3-lower-2.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_family_rank1.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": null }, { "slug": "cat-m3-upper-2", "file": "bounds/cat-m3-upper-2.json", "orbit": "cat", "m": 3, "direction": "upper", "rank": 2, "tier": "verified", "ok": true, "date": "2021-06-14", "author": "Qassim, Pashayan, and Gosset", "reference": "arXiv:2106.07740", "method": "literature", "pull_request": 141, "merge_commit": "17b9c1f584f9784436d271c763fbe07ef7bf3c6c", "merge_date": "2026-09-24", "added_commit": "e84a236183ba4a9df078a6f52c71e66043e47ad9", "added_date": "2026-09-24", "added_subject": "Add the magic cat track: cat_m targets, implied H exponent, and the QPG cells", "receipt": "certs/cat-m3-upper-2.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": null }, { "slug": "cat-m4-lower-2", "file": "bounds/cat-m4-lower-2.json", "orbit": "cat", "m": 4, "direction": "lower", "rank": 2, "tier": "verified", "ok": true, "date": "2026-09-24", "author": "this repository", "reference": "stabrank verify_challenge", "method": "exact: the state is not a stabilizer state (its phase on the even-weight strings is not a Z_4 quadratic form)", "pull_request": 141, "merge_commit": "17b9c1f584f9784436d271c763fbe07ef7bf3c6c", "merge_date": "2026-09-24", "added_commit": "e84a236183ba4a9df078a6f52c71e66043e47ad9", "added_date": "2026-09-24", "added_subject": "Add the magic cat track: cat_m targets, implied H exponent, and the QPG cells", "receipt": "certs/cat-m4-lower-2.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_family_rank1.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": null }, { "slug": "cat-m4-upper-2", "file": "bounds/cat-m4-upper-2.json", "orbit": "cat", "m": 4, "direction": "upper", "rank": 2, "tier": "verified", "ok": true, "date": "2021-06-14", "author": "Qassim, Pashayan, and Gosset", "reference": "arXiv:2106.07740", "method": "literature", "pull_request": 141, "merge_commit": "17b9c1f584f9784436d271c763fbe07ef7bf3c6c", "merge_date": "2026-09-24", "added_commit": "e84a236183ba4a9df078a6f52c71e66043e47ad9", "added_date": "2026-09-24", "added_subject": "Add the magic cat track: cat_m targets, implied H exponent, and the QPG cells", "receipt": "certs/cat-m4-upper-2.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": null }, { "slug": "cat-m5-lower-3", "file": "bounds/cat-m5-lower-3.json", "orbit": "cat", "m": 5, "direction": "lower", "rank": 3, "tier": "verified", "ok": true, "date": "2026-10-16", "author": "Michel de Messieres", "reference": "stabrank verify_challenge", "method": "exact rank-2 exclusion over the 36,720 four-qubit stabilizer states after compressing |cat_5> into the even-weight code Z^5 = +1", "pull_request": 141, "merge_commit": "17b9c1f584f9784436d271c763fbe07ef7bf3c6c", "merge_date": "2026-09-24", "added_commit": "e84a236183ba4a9df078a6f52c71e66043e47ad9", "added_date": "2026-09-24", "added_subject": "Add the magic cat track: cat_m targets, implied H exponent, and the QPG cells", "receipt": "certs/cat-m5-lower-3.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_cat_m5_rank2.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.01, "wall_clock_hours": 0.01, "runs": 3, "hardware": "Apple silicon laptop, one core", "llm": [ { "model": "claude-opus-5-5", "role": "designed, wrote and ran the certificate and its cross-checks" } ] } }, { "slug": "cat-m5-upper-3", "file": "bounds/cat-m5-upper-3.json", "orbit": "cat", "m": 5, "direction": "upper", "rank": 3, "tier": "verified", "ok": true, "date": "2021-06-14", "author": "Qassim, Pashayan, and Gosset", "reference": "arXiv:2106.07740", "method": "literature", "pull_request": 141, "merge_commit": "17b9c1f584f9784436d271c763fbe07ef7bf3c6c", "merge_date": "2026-09-24", "added_commit": "e84a236183ba4a9df078a6f52c71e66043e47ad9", "added_date": "2026-09-24", "added_subject": "Add the magic cat track: cat_m targets, implied H exponent, and the QPG cells", "receipt": "certs/cat-m5-upper-3.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": null }, { "slug": "cat-m6-lower-3", "file": "bounds/cat-m6-lower-3.json", "orbit": "cat", "m": 6, "direction": "lower", "rank": 3, "tier": "verified", "ok": true, "date": "2026-10-16", "author": "Michel de Messieres", "reference": "stabrank verify_challenge", "method": "projection monotonicity applied to the exact rank-2 exclusion at m=5", "pull_request": 141, "merge_commit": "17b9c1f584f9784436d271c763fbe07ef7bf3c6c", "merge_date": "2026-09-24", "added_commit": "e84a236183ba4a9df078a6f52c71e66043e47ad9", "added_date": "2026-09-24", "added_subject": "Add the magic cat track: cat_m targets, implied H exponent, and the QPG cells", "receipt": "certs/cat-m6-lower-3.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_cat_m5_rank2.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0, "wall_clock_hours": 0, "runs": 0, "hardware": "none beyond the m=5 certificate, which this cell re-runs" } }, { "slug": "cat-m6-upper-3", "file": "bounds/cat-m6-upper-3.json", "orbit": "cat", "m": 6, "direction": "upper", "rank": 3, "tier": "verified", "ok": true, "date": "2021-06-14", "author": "Qassim, Pashayan, and Gosset", "reference": "arXiv:2106.07740", "method": "literature", "pull_request": 141, "merge_commit": "17b9c1f584f9784436d271c763fbe07ef7bf3c6c", "merge_date": "2026-09-24", "added_commit": "e84a236183ba4a9df078a6f52c71e66043e47ad9", "added_date": "2026-09-24", "added_subject": "Add the magic cat track: cat_m targets, implied H exponent, and the QPG cells", "receipt": "certs/cat-m6-upper-3.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": null }, { "slug": "cat-m7-lower-3", "file": "bounds/cat-m7-lower-3.json", "orbit": "cat", "m": 7, "direction": "lower", "rank": 3, "tier": "cited", "ok": true, "date": "2021-06-14", "author": "Qassim, Pashayan, and Gosset", "reference": "arXiv:2106.07740", "method": "literature", "pull_request": 141, "merge_commit": "17b9c1f584f9784436d271c763fbe07ef7bf3c6c", "merge_date": "2026-09-24", "added_commit": "e84a236183ba4a9df078a6f52c71e66043e47ad9", "added_date": "2026-09-24", "added_subject": "Add the magic cat track: cat_m targets, implied H exponent, and the QPG cells", "receipt": null, "receipt_matches": null, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": null }, { "slug": "cat-m7-lower-4", "file": "bounds/cat-m7-lower-4.json", "orbit": "cat", "m": 7, "direction": "lower", "rank": 4, "tier": "verified", "ok": true, "date": "2026-10-16", "author": "Michel de Messieres", "reference": "stabrank verify_challenge", "method": "slice-and-lift in the even-weight compressed picture: the one rank-3 decomposition of compressed cat_6 up to symmetry does not extend to cat_7", "pull_request": 170, "merge_commit": "7bf45fea9ed8d08c511aba8c121c33ca4446bc0f", "merge_date": "2026-10-17", "added_commit": "22939a2cff993daadc7685566e182af2888e3bd7", "added_date": "2026-10-16", "added_subject": "Certify cat lower bounds: chi(cat_5,6) >= 3, chi(cat_7,8) >= 4", "receipt": "certs/cat-m7-lower-4.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_cat_m7_lift.py", "certificate_budget_s": 1800, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 2.8, "wall_clock_hours": 2.5, "runs": 5, "hardware": "Apple silicon laptop, one core per run", "llm": [ { "model": "claude-opus-5-5", "role": "designed, wrote and ran the certificate and its cross-checks" } ] } }, { "slug": "cat-m7-lower-5", "file": "bounds/cat-m7-lower-5.json", "orbit": "cat", "m": 7, "direction": "lower", "rank": 5, "tier": "attested", "ok": true, "date": "2026-10-17", "author": "Vincent Russo", "reference": "stabrank-research, round 31 (attacks/round31-J-lower-bounds)", "method": "two-qubit base slice of the even-weight compressed cat_7: every rank-4 decomposition has three or four terms visible at the base point; the bases (a census of full 4-covers of compressed cat_5, the rank-3 decompositions with an invisible, dependent or repeated term) are completed point by point under the qubit slice structure lemma and nothing completes", "pull_request": 178, "merge_commit": "a3f179f7529639689e9f82c6d8276ae825cefa9f", "merge_date": "2026-10-21", "added_commit": "37dbae082831a4ae9f3bb64e4dbd6b2deeceda55", "added_date": "2026-10-21", "added_subject": "Lower bounds chi(cat_7) >= 5 and chi(cat_8) >= 5 (attested): two-qubit base-slice exclusion of rank 4 for the compressed cat_7 state", "receipt": "certs/cat-m7-lower-5.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_cat_m7_rank4_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/cat7_rank4/batch_manifest.json", "recomputed": 2, "compute_hours": 110.9, "hardware": "one Perlmutter CPU node (AMD EPYC 7763, 128 workers) for the corrected census of the full 4-covers of compressed cat_5, job 59930310, 1261 s wall, 2026-10-18 UTC; two earlier census runs (jobs 59924919 and 59926124, 736 s and 1,120 s) listed a fifth of the covers because their hash functionals wrapped int64 and are superseded; stages beta, B, C and A on an Apple silicon laptop (one core)", "note": "The census lists every 4-set of four-qubit stabilizer states whose span contains c_5 = cat_5(y, parity(y)) with four nonzero coefficients and independent states, one per orbit of the group generated by permutations of the four qubits, R(x)R on a pair and the parity swap of cat_7 (100 pivot orbits, 2,292,776 pivot pairs, 16,705 covers), stored per work unit (pivot orbit, partner stride class, 1,600 batches) under research/cat7_rank4/results/. The certificate verifies every stored batch hash, re-enumerates two units from scratch (seed 20261017) and compares, then runs the whole exclusion: stages beta (one invisible term), B (dependent bases: none exist), C (a repeated base state) and A (the stored covers), with every candidate completion rebuilt and decided exactly; a decomposition with fewer than four terms would fail the run. The census functionals reduce every product modulo P before summing (research/cat7_rank4/census_control.py plants targets: the corrected functional lists all ten, the wrapped one none). Completeness of the census rests on the stored outputs and on research/cat7_rank4/census4_run.py, which regenerates any unit.", "total": 1600 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 111.7, "wall_clock_hours": 4.0, "runs": 6, "hardware": "one Perlmutter CPU node (AMD EPYC 7763, 128 workers, 1,261 s) for the corrected census of the full 4-covers of compressed cat_5, after two superseded census runs (736 s and 1,120 s) whose hash functionals wrapped int64; Apple silicon laptop for the completion stages, the exact confirmation and the controls", "llm": [ { "model": "claude-fable-5-1", "role": "designed, wrote and ran the exclusion and its planted controls" } ] } }, { "slug": "cat-m7-upper-6", "file": "bounds/cat-m7-upper-6.json", "orbit": "cat", "m": 7, "direction": "upper", "rank": 6, "tier": "verified", "ok": true, "date": "2021-06-14", "author": "Qassim, Pashayan, and Gosset", "reference": "arXiv:2106.07740", "method": "literature", "pull_request": 141, "merge_commit": "17b9c1f584f9784436d271c763fbe07ef7bf3c6c", "merge_date": "2026-09-24", "added_commit": "e84a236183ba4a9df078a6f52c71e66043e47ad9", "added_date": "2026-09-24", "added_subject": "Add the magic cat track: cat_m targets, implied H exponent, and the QPG cells", "receipt": "certs/cat-m7-upper-6.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": null }, { "slug": "cat-m8-lower-3", "file": "bounds/cat-m8-lower-3.json", "orbit": "cat", "m": 8, "direction": "lower", "rank": 3, "tier": "cited", "ok": true, "date": "2021-06-14", "author": "Qassim, Pashayan, and Gosset", "reference": "arXiv:2106.07740", "method": "literature", "pull_request": 141, "merge_commit": "17b9c1f584f9784436d271c763fbe07ef7bf3c6c", "merge_date": "2026-09-24", "added_commit": "e84a236183ba4a9df078a6f52c71e66043e47ad9", "added_date": "2026-09-24", "added_subject": "Add the magic cat track: cat_m targets, implied H exponent, and the QPG cells", "receipt": null, "receipt_matches": null, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": null }, { "slug": "cat-m8-lower-4", "file": "bounds/cat-m8-lower-4.json", "orbit": "cat", "m": 8, "direction": "lower", "rank": 4, "tier": "verified", "ok": true, "date": "2026-10-16", "author": "Michel de Messieres", "reference": "stabrank verify_challenge", "method": "projection monotonicity applied to the slice-and-lift exclusion chi(cat_7) >= 4", "pull_request": 170, "merge_commit": "7bf45fea9ed8d08c511aba8c121c33ca4446bc0f", "merge_date": "2026-10-17", "added_commit": "22939a2cff993daadc7685566e182af2888e3bd7", "added_date": "2026-10-16", "added_subject": "Certify cat lower bounds: chi(cat_5,6) >= 3, chi(cat_7,8) >= 4", "receipt": "certs/cat-m8-lower-4.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_cat_m7_lift.py", "certificate_budget_s": 1800, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0, "wall_clock_hours": 0, "runs": 0, "hardware": "none beyond the m=7 certificate, which this cell re-runs" } }, { "slug": "cat-m8-lower-5", "file": "bounds/cat-m8-lower-5.json", "orbit": "cat", "m": 8, "direction": "lower", "rank": 5, "tier": "attested", "ok": true, "date": "2026-10-17", "author": "Vincent Russo", "reference": "stabrank-research, round 31 (attacks/round31-J-lower-bounds)", "method": "projection monotonicity applied to the rank-4 exclusion at m = 7: (I (x) <0|) cat_8 = 2^(-1/2) cat_7 exactly and <0| maps a stabilizer state to a stabilizer state or zero", "pull_request": 178, "merge_commit": "a3f179f7529639689e9f82c6d8276ae825cefa9f", "merge_date": "2026-10-21", "added_commit": "37dbae082831a4ae9f3bb64e4dbd6b2deeceda55", "added_date": "2026-10-21", "added_subject": "Lower bounds chi(cat_7) >= 5 and chi(cat_8) >= 5 (attested): two-qubit base-slice exclusion of rank 4 for the compressed cat_7 state", "receipt": "certs/cat-m8-lower-5.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_cat_m7_rank4_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/cat7_rank4/batch_manifest.json", "recomputed": 2, "compute_hours": 110.9, "hardware": "one Perlmutter CPU node (AMD EPYC 7763, 128 workers) for the corrected census of the full 4-covers of compressed cat_5, job 59930310, 1261 s wall, 2026-10-18 UTC; two earlier census runs (jobs 59924919 and 59926124, 736 s and 1,120 s) listed a fifth of the covers because their hash functionals wrapped int64 and are superseded; stages beta, B, C and A on an Apple silicon laptop (one core)", "note": "The census lists every 4-set of four-qubit stabilizer states whose span contains c_5 = cat_5(y, parity(y)) with four nonzero coefficients and independent states, one per orbit of the group generated by permutations of the four qubits, R(x)R on a pair and the parity swap of cat_7 (100 pivot orbits, 2,292,776 pivot pairs, 16,705 covers), stored per work unit (pivot orbit, partner stride class, 1,600 batches) under research/cat7_rank4/results/. The certificate verifies every stored batch hash, re-enumerates two units from scratch (seed 20261017) and compares, then runs the whole exclusion: stages beta (one invisible term), B (dependent bases: none exist), C (a repeated base state) and A (the stored covers), with every candidate completion rebuilt and decided exactly; a decomposition with fewer than four terms would fail the run. The census functionals reduce every product modulo P before summing (research/cat7_rank4/census_control.py plants targets: the corrected functional lists all ten, the wrapped one none). Completeness of the census rests on the stored outputs and on research/cat7_rank4/census4_run.py, which regenerates any unit.", "total": 1600 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 111.7, "wall_clock_hours": 4.0, "runs": 6, "hardware": "none beyond the m=7 certificate, which this cell re-runs" } }, { "slug": "cat-m8-upper-6", "file": "bounds/cat-m8-upper-6.json", "orbit": "cat", "m": 8, "direction": "upper", "rank": 6, "tier": "verified", "ok": true, "date": "2021-06-14", "author": "Qassim, Pashayan, and Gosset", "reference": "arXiv:2106.07740", "method": "literature", "pull_request": 141, "merge_commit": "17b9c1f584f9784436d271c763fbe07ef7bf3c6c", "merge_date": "2026-09-24", "added_commit": "e84a236183ba4a9df078a6f52c71e66043e47ad9", "added_date": "2026-09-24", "added_subject": "Add the magic cat track: cat_m targets, implied H exponent, and the QPG cells", "receipt": "certs/cat-m8-upper-6.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": null }, { "slug": "qubit_H-m1-lower-2", "file": "bounds/qubit_H-m1-lower-2.json", "orbit": "qubit_H", "m": 1, "direction": "lower", "rank": 2, "tier": "verified", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank verify_challenge", "method": "exact: the state is not a stabilizer state (the moduli cos(pi/8) and sin(pi/8) differ)", "pull_request": 177, "merge_commit": "2fffdf2d28dafba398e4162820f9df00b1eefefb", "merge_date": "2026-10-21", "added_commit": "dd232c348dfd99d3339e2e11dcad6749b7bc27e9", "added_date": "2026-10-21", "added_subject": "File the single-copy cells of H3, N, qubit_H, and qubit_T", "receipt": "certs/qubit_H-m1-lower-2.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_rank1_moduli.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": null }, { "slug": "qubit_H-m1-upper-2", "file": "bounds/qubit_H-m1-upper-2.json", "orbit": "qubit_H", "m": 1, "direction": "upper", "rank": 2, "tier": "verified", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank research/constructions/data", "method": "direct construction: the single-copy state as a combination of two stabilizer states", "pull_request": 177, "merge_commit": "2fffdf2d28dafba398e4162820f9df00b1eefefb", "merge_date": "2026-10-21", "added_commit": "dd232c348dfd99d3339e2e11dcad6749b7bc27e9", "added_date": "2026-10-21", "added_subject": "File the single-copy cells of H3, N, qubit_H, and qubit_T", "receipt": "certs/qubit_H-m1-upper-2.json", "receipt_matches": true, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "qubit_H-m10-lower-6", "file": "bounds/qubit_H-m10-lower-6.json", "orbit": "qubit_H", "m": 10, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-09-22", "author": "this repository", "reference": "stabrank research/h6_rank5", "method": "projection monotonicity applied to the attested exact rank-5 exclusion at m=6", "pull_request": 102, "merge_commit": "940bbc3f5061af0b0c86aad7f5debc49e77ae683", "merge_date": "2026-09-22", "added_commit": "c7155b380cbd0232d30d52f8eeeb2c131536964c", "added_date": "2026-09-22", "added_subject": "Project chi(H^6) >= 6 to the m = 7, 8, and 10 cells at the attested tier", "receipt": "certs/qubit_H-m10-lower-6.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_h_m6_rank5_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/h6_rank5/batch_manifest.json", "recomputed": 2, "compute_hours": 73.4, "hardware": "187 batches on a RunPod CPU pod (16 vCPU AMD EPYC 4564P, shared host at load 30 to 45, ten batches in parallel, nice 19), 2026-09-22 01:37 to 08:31 UTC; batches 14, 15, and 173 on an Apple silicon laptop (one core, nice 19) during the pipeline test on 2026-09-21; the aggregate's two seeded re-runs (batches 11 and 148) on the pod", "note": "The exclusion of every rank-5 decomposition of |H>^6 lives in the 190 stored batch outputs under research/h6_rank5/results/ (15 stage A batches over the 5,939,465 full 5-covers of |H>^3 with distinct independent base states, 158 stage B batches over the 12,390 dependent covers, 17 stage C batches over the 13,852 covers with a repeated state), each matching its covers at the four base points and re-deciding every candidate mod 2013265921 and numerically. The certificate checks the partition against the enumerator, re-enumerates the degenerate covers, verifies the hashes and geometry of every output, re-decides every stored hit, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/h6_rank5/batch.py, which regenerates any batch (`batch.py K`, 73.4 CPU-hours for all 190 on the pod: stage A 2.8, stage B 69.6, stage C 1.0).", "total": 180 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=6 certificate, which this cell re-runs" } }, { "slug": "qubit_H-m10-upper-18", "file": "bounds/qubit_H-m10-upper-18.json", "orbit": "qubit_H", "m": 10, "direction": "upper", "rank": 18, "tier": "lean", "ok": true, "date": "2022-02-18", "author": "Kissinger, van de Wetering, and Vilmart", "reference": "arXiv:2202.09202", "method": "literature", "pull_request": 83, "merge_commit": "e02f55453136aaba1d76fefb222c48eb29eb4ac9", "merge_date": "2026-09-21", "added_commit": "7b14437ef9eafdc34c2c5d3af161bff419a8e6b2", "added_date": "2026-09-21", "added_subject": "Add the Kissinger, van de Wetering, and Vilmart cells for qubit_H at m = 7, 8, 10", "receipt": "certs/qubit_H-m10-upper-18.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.QubitHM10StabRank", "lean_theorem": "qubit_h_m10_stabRankP_le_eighteen", "lean_receipt": "certs/lean-LeanProofs-QubitHM10StabRank.json", "lean_receipt_ok": true, "compute": { "cpu_hours": 0.01, "wall_clock_hours": 0.01, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "qubit_H-m2-lower-2", "file": "bounds/qubit_H-m2-lower-2.json", "orbit": "qubit_H", "m": 2, "direction": "lower", "rank": 2, "tier": "lean", "ok": true, "date": "2026-09-20", "author": "this repository", "reference": "stabrank verify_challenge", "method": "exact: the state is not a stabilizer state (two distinct amplitude moduli)", "pull_request": 61, "merge_commit": "fec578fb6ad236de4564d49145a619b4924bd963", "merge_date": "2026-09-20", "added_commit": "801680d49c63f74d82974b5bab3f9b566965b959", "added_date": "2026-09-20", "added_subject": "Lower bounds for the five cells that had none", "receipt": "certs/qubit_H-m2-lower-2.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_rank1_moduli.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.QubitM2Lower", "lean_theorem": "qubit_h_m2_stabRankP_gt_one", "lean_receipt": "certs/lean-LeanProofs-QubitM2Lower.json", "lean_receipt_ok": true, "compute": null }, { "slug": "qubit_H-m2-upper-2", "file": "bounds/qubit_H-m2-upper-2.json", "orbit": "qubit_H", "m": 2, "direction": "upper", "rank": 2, "tier": "lean", "ok": true, "date": "2015-06-03", "author": "Bravyi, Smith, and Smolin", "reference": "arXiv:1506.01396", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": "certs/qubit_H-m2-upper-2.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.QubitHStabRank", "lean_theorem": "qubit_h_m2_stabRankP_le_two", "lean_receipt": "certs/lean-LeanProofs-QubitHStabRank.json", "lean_receipt_ok": true, "compute": { "cpu_hours": 0.01, "wall_clock_hours": 0.01, "runs": 1, "hardware": "Apple silicon laptop, 8 annealing chains" } }, { "slug": "qubit_H-m3-lower-3", "file": "bounds/qubit_H-m3-lower-3.json", "orbit": "qubit_H", "m": 3, "direction": "lower", "rank": 3, "tier": "reproduced", "ok": true, "date": "2026-09-12", "author": "this repository", "reference": "stabrank PR #18", "method": "exhaustion over all pairs of stabilizer states, via the quotient by the target", "pull_request": 18, "merge_commit": "293f15c35bdf189751f6e2b8cf833f535d04f287", "merge_date": "2026-09-16", "added_commit": "2fad4bd18188a4f950ae84661a03ffa307f7eca5", "added_date": "2026-09-12", "added_subject": "Close the qubit rank-2 cells too", "receipt": "certs/qubit_H-m3-lower-3.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_rank2.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": null }, { "slug": "qubit_H-m3-upper-3", "file": "bounds/qubit_H-m3-upper-3.json", "orbit": "qubit_H", "m": 3, "direction": "upper", "rank": 3, "tier": "lean", "ok": true, "date": "2015-06-03", "author": "Bravyi, Smith, and Smolin", "reference": "arXiv:1506.01396", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": "certs/qubit_H-m3-upper-3.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.QubitHStabRank", "lean_theorem": "qubit_h_m3_stabRankP_le_three", "lean_receipt": "certs/lean-LeanProofs-QubitHStabRank.json", "lean_receipt_ok": true, "compute": { "cpu_hours": 0.01, "wall_clock_hours": 0.01, "runs": 1, "hardware": "Apple silicon laptop, 8 annealing chains" } }, { "slug": "qubit_H-m4-lower-3", "file": "bounds/qubit_H-m4-lower-3.json", "orbit": "qubit_H", "m": 4, "direction": "lower", "rank": 3, "tier": "reproduced", "ok": true, "date": "2026-09-12", "author": "this repository", "reference": "stabrank PR #18", "method": "exhaustion over all pairs of stabilizer states, via the quotient by the target", "pull_request": 18, "merge_commit": "293f15c35bdf189751f6e2b8cf833f535d04f287", "merge_date": "2026-09-16", "added_commit": "2fad4bd18188a4f950ae84661a03ffa307f7eca5", "added_date": "2026-09-12", "added_subject": "Close the qubit rank-2 cells too", "receipt": "certs/qubit_H-m4-lower-3.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_rank2.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": null }, { "slug": "qubit_H-m4-lower-4", "file": "bounds/qubit_H-m4-lower-4.json", "orbit": "qubit_H", "m": 4, "direction": "lower", "rank": 4, "tier": "reproduced", "ok": true, "date": "2026-09-16", "author": "this repository", "reference": "stabrank rank_exclusion.py", "method": "exhaustion over all triples of 4-qubit stabilizer states, via a pivot and two quotients", "pull_request": 24, "merge_commit": "7e72a78cefefa660acca809d2c7275424fb32258", "merge_date": "2026-09-17", "added_commit": "19fd51cfa2a46b7c8c818baefa784842d97b07d7", "added_date": "2026-09-16", "added_subject": "Certify nine lower bounds: five cells settled, T3 at m=4 bounded for the first time", "receipt": "certs/qubit_H-m4-lower-4.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_h_m4_rank3.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.3, "wall_clock_hours": 0.08, "runs": 1, "hardware": "Apple silicon laptop, 8 worker processes" } }, { "slug": "qubit_H-m4-upper-4", "file": "bounds/qubit_H-m4-upper-4.json", "orbit": "qubit_H", "m": 4, "direction": "upper", "rank": 4, "tier": "lean", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": "certs/qubit_H-m4-upper-4.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.QubitHStabRank", "lean_theorem": "qubit_h_m4_stabRankP_le_four", "lean_receipt": "certs/lean-LeanProofs-QubitHStabRank.json", "lean_receipt_ok": true, "compute": { "cpu_hours": 0.01, "wall_clock_hours": 0.01, "runs": 1, "hardware": "Apple silicon laptop, 8 annealing chains" } }, { "slug": "qubit_H-m5-lower-4", "file": "bounds/qubit_H-m5-lower-4.json", "orbit": "qubit_H", "m": 5, "direction": "lower", "rank": 4, "tier": "reproduced", "ok": true, "date": "2026-09-18", "author": "this repository", "reference": "stabrank rank_exclusion.py", "method": "projection monotonicity applied to an exhaustive exclusion at lower m", "pull_request": 51, "merge_commit": "4e2a9643ac1e2516dc0c02d7a8242018a337f2d7", "merge_date": "2026-09-18", "added_commit": "ec8223833bcfbf50a44317943d4d9800a19d4139", "added_date": "2026-09-18", "added_subject": "Fix the documentation drift the M5 draft surfaced", "receipt": "certs/qubit_H-m5-lower-4.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_h_m6_from_m4.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.02, "wall_clock_hours": 0.01, "runs": 1, "hardware": "Apple silicon laptop; the m=4 rank-3 exclusion re-runs inside the certificate" } }, { "slug": "qubit_H-m5-lower-5", "file": "bounds/qubit_H-m5-lower-5.json", "orbit": "qubit_H", "m": 5, "direction": "lower", "rank": 5, "tier": "reproduced", "ok": true, "date": "2026-09-18", "author": "this repository", "reference": "stabrank slice_lift.py", "method": "slice-and-lift: none of the 30 rank-4 decompositions of |H>^4 up to symmetry extends to |H>^5", "pull_request": 56, "merge_commit": "7ecdfa9075bbf0d2d5e6545d5e025ada7a585c61", "merge_date": "2026-09-19", "added_commit": "3fe935de6e06c3f9da5ff8455ef56e47a55d4cfb", "added_date": "2026-09-18", "added_subject": "chi(H^5) >= 5 for the qubit H-type state by slice-and-lift", "receipt": "certs/qubit_H-m5-lower-5.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_h_m5_lift.py", "certificate_budget_s": 3600, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 1.9, "wall_clock_hours": 0.46, "runs": 1, "hardware": "Apple silicon laptop, four workers at low priority under a load average near 12: 1649 s for the enumeration and lift" } }, { "slug": "qubit_H-m5-lower-6", "file": "bounds/qubit_H-m5-lower-6.json", "orbit": "qubit_H", "m": 5, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-09-24", "author": "this repository", "reference": "stabrank research/h5_rank5", "method": "two-qubit base slice: every rank-5 decomposition of |H>^5 has, along qubits 1, 2 at a base point in {00, 01}, either all five terms visible (a full 5-cover of |H>^3, the H^6 census) or four visible and one line term on the diagonal missing the base point (a full 4-cover of |H>^3); every base is completed slice by slice under the slice structure lemma, modulo 65521 with exact re-decision", "pull_request": 125, "merge_commit": "e99761ff5ccfde8e454bd6353f59c57509d4b786", "merge_date": "2026-09-23", "added_commit": "a8f9488efc810e56d63576a5e2148581238613f4", "added_date": "2026-09-23", "added_subject": "chi(H^5) >= 6: the rank-5 exclusion run, its batch manifest, and the attested bound", "receipt": "certs/qubit_H-m5-lower-6.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_h_m5_rank5_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/h5_rank5/batch_manifest.json", "recomputed": 2, "compute_hours": 37.2, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host (load 25 to 40), fifteen batches in parallel at nice 19, 2026-09-23 21:56 to 2026-09-24 00:28 UTC (stage A probe batch 0 at 21:56, the 323-batch run 22:02 to 00:28); the aggregate's two seeded re-runs (batches 19 and 319) on the same pod at 00:28 UTC", "note": "The exclusion of every rank-5 decomposition of |H>^5 lives in the stored batch outputs under research/h5_rank5/results/ (partition.json: 16 stage A batches over the 5,939,465 full 5-covers of |H>^3 with distinct independent base states, 293 stage B batches over the 12,390 dependent covers, 9 stage C batches over the 16,006 covers with a repeated state, including the cancel-at-base multisets, and 5 stage beta batches over the 3,466 full 4-covers, 6 of them with a repeated state), each cover matched at the base points 00 and 01 along qubits 1, 2 and every candidate re-decided mod 2013265921 and numerically: 0 hits, 0 refused, 0 undecided. The certificate checks the partition against the enumerator and the census hash, re-enumerates the degenerate covers and the stage beta bases, verifies the hashes and geometry of every output, re-decides every stored hit, fails on any refusal or undecided run, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/h5_rank5/batch.py, which regenerates any batch (batch.py K).", "total": 323 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 37.2, "wall_clock_hours": 2.5, "runs": 1, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host (load 25 to 40), fifteen batches in parallel at nice 19, 2026-09-23 21:56 to 2026-09-24 00:28 UTC (stage A probe batch 0 at 21:56, the 323-batch run 22:02 to 00:28); the aggregate's two seeded re-runs (batches 19 and 319) on the same pod at 00:28 UTC" } }, { "slug": "qubit_H-m5-upper-6", "file": "bounds/qubit_H-m5-upper-6.json", "orbit": "qubit_H", "m": 5, "direction": "upper", "rank": 6, "tier": "lean", "ok": true, "date": "2015-06-03", "author": "Bravyi, Smith, and Smolin", "reference": "arXiv:1506.01396", "method": "literature", "pull_request": 23, "merge_commit": "4ef357db2e821e5d4c5d518d2895a59288cdb85f", "merge_date": "2026-09-17", "added_commit": "e99b00d2043d06cd85d532ada9ca3960cccfdda0", "added_date": "2026-09-16", "added_subject": "Restore chi(H^6) <= 6, attributed to Qassim, Pashayan and Gosset, with a witness", "receipt": "certs/qubit_H-m5-upper-6.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.QubitHM5StabRank", "lean_theorem": "qubit_h_m5_stabRankP_le_six", "lean_receipt": "certs/lean-LeanProofs-QubitHM5StabRank.json", "lean_receipt_ok": true, "compute": { "cpu_hours": 0.02, "wall_clock_hours": 0.02, "runs": 1, "hardware": "Apple silicon laptop, 8 annealing chains" } }, { "slug": "qubit_H-m6-lower-4", "file": "bounds/qubit_H-m6-lower-4.json", "orbit": "qubit_H", "m": 6, "direction": "lower", "rank": 4, "tier": "reproduced", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": "certs/qubit_H-m6-lower-4.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_h_m6_from_m4.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.3, "wall_clock_hours": 0.08, "runs": 1, "hardware": "Apple silicon laptop, 8 worker processes" } }, { "slug": "qubit_H-m6-lower-6", "file": "bounds/qubit_H-m6-lower-6.json", "orbit": "qubit_H", "m": 6, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-09-23", "author": "this repository", "reference": "stabrank research/h6_rank5", "method": "all-visible base slice: every rank-5 decomposition of |H>^6 restricts, along some three qubits at some base point, to a full 5-cover of |H>^3 with all five terms nonzero; every such cover is enumerated up to symmetry and completed slice by slice under the slice structure lemma, modulo 65521 with exact re-decision", "pull_request": 89, "merge_commit": "24d020a3b430892a00411065b01e3f33757d8fa0", "merge_date": "2026-09-22", "added_commit": "8bfb853e19b1654f040daa1966fa2d390d50ffbc", "added_date": "2026-09-22", "added_subject": "chi(H^6) = 6: the rank-5 exclusion run, its batch manifest, and the attested bound", "receipt": "certs/qubit_H-m6-lower-6.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_h_m6_rank5_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/h6_rank5/batch_manifest.json", "recomputed": 2, "compute_hours": 74.7, "hardware": "187 batches on a RunPod CPU pod (16 vCPU AMD EPYC 4564P, shared host at load 30 to 45, ten batches in parallel, nice 19), 2026-09-22 01:37 to 08:31 UTC; batches 14, 15, and 173 on an Apple silicon laptop (one core, nice 19) during the pipeline test on 2026-09-21; the aggregate's two seeded re-runs (batches 11 and 148) on the pod; the stage C repair batches 190 to 196 on the same pod (seven in parallel, nice 19), 2026-09-23 09:17 to 09:32 UTC, and the aggregate's two seeded re-runs (batches 10 and 140) on the pod afterwards", "note": "The exclusion of every rank-5 decomposition of |H>^6 lives in 180 stored batch outputs under research/h6_rank5/results/: 15 stage A batches over the 5,939,465 full 5-covers of |H>^3 with distinct independent base states, 158 stage B batches over the 12,390 dependent covers (partition.json, batches 0 to 172), and the 7 stage C repair batches 190 to 196 (partition_stage_c_v2.json) over the 16,006 covers with a repeated state of the regenerated list degenerate_covers_v2.json, which supersede the 17 original stage C batches 173 to 189 over 13,852 covers (docs/notes/h6_rank5_stagec_repair.md: the original list missed the 2,154 multisets T + (b, b) with b outside span(T), and the block reconstruction missed cancelling copies). Each batch matches its covers at the four base points and re-decides every candidate mod 2013265921 and numerically. The certificate checks both partitions against the enumerator, re-enumerates the degenerate covers into the regenerated list, verifies the hashes and geometry of every output, re-decides every stored hit, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/h6_rank5/batch.py, which regenerates any batch (`batch.py K`, with --partition research/h6_rank5/partition_stage_c_v2.json for 190 to 196): 74.7 CPU-hours on the pod, stage A 2.8, stage B 69.6, stage C 1.3.", "total": 180 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 74.7, "wall_clock_hours": 7.2, "runs": 2, "hardware": "187 batches on a RunPod CPU pod (16 vCPU AMD EPYC 4564P, shared host at load 30 to 45, ten batches in parallel, nice 19), 2026-09-22 01:37 to 08:31 UTC; batches 14, 15, and 173 on an Apple silicon laptop (one core, nice 19) during the pipeline test on 2026-09-21; the aggregate's two seeded re-runs (batches 11 and 148) on the pod; the stage C repair batches 190 to 196 on the same pod (seven in parallel, nice 19), 2026-09-23 09:17 to 09:32 UTC, and the aggregate's two seeded re-runs (batches 10 and 140) on the pod afterwards" } }, { "slug": "qubit_H-m6-upper-6", "file": "bounds/qubit_H-m6-upper-6.json", "orbit": "qubit_H", "m": 6, "direction": "upper", "rank": 6, "tier": "lean", "ok": true, "date": "2021-06-14", "author": "Qassim, Pashayan, and Gosset", "reference": "arXiv:2106.07740", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": "certs/qubit_H-m6-upper-6.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.QubitHM6StabRank", "lean_theorem": "qubit_h_m6_stabRankP_le_six", "lean_receipt": "certs/lean-LeanProofs-QubitHM6StabRank.json", "lean_receipt_ok": true, "compute": null }, { "slug": "qubit_H-m6-upper-7", "file": "bounds/qubit_H-m6-upper-7.json", "orbit": "qubit_H", "m": 6, "direction": "upper", "rank": 7, "tier": "verified", "ok": true, "date": "2015-06-03", "author": "Bravyi, Smith, and Smolin", "reference": "arXiv:1506.01396", "method": "literature", "pull_request": 23, "merge_commit": "4ef357db2e821e5d4c5d518d2895a59288cdb85f", "merge_date": "2026-09-17", "added_commit": "c1a03fe3f58032297193e88fcb709a5a7facebea", "added_date": "2026-09-16", "added_subject": "Give every cited upper bound a verified witness, and correct qubit_H at m=6", "receipt": "certs/qubit_H-m6-upper-7.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.1, "wall_clock_hours": 0.1, "runs": 3, "hardware": "Apple silicon laptop, 8 annealing chains per run" } }, { "slug": "qubit_H-m7-lower-6", "file": "bounds/qubit_H-m7-lower-6.json", "orbit": "qubit_H", "m": 7, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-09-22", "author": "this repository", "reference": "stabrank research/h6_rank5", "method": "projection monotonicity applied to the attested exact rank-5 exclusion at m=6", "pull_request": 102, "merge_commit": "940bbc3f5061af0b0c86aad7f5debc49e77ae683", "merge_date": "2026-09-22", "added_commit": "c7155b380cbd0232d30d52f8eeeb2c131536964c", "added_date": "2026-09-22", "added_subject": "Project chi(H^6) >= 6 to the m = 7, 8, and 10 cells at the attested tier", "receipt": "certs/qubit_H-m7-lower-6.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_h_m6_rank5_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/h6_rank5/batch_manifest.json", "recomputed": 2, "compute_hours": 73.4, "hardware": "187 batches on a RunPod CPU pod (16 vCPU AMD EPYC 4564P, shared host at load 30 to 45, ten batches in parallel, nice 19), 2026-09-22 01:37 to 08:31 UTC; batches 14, 15, and 173 on an Apple silicon laptop (one core, nice 19) during the pipeline test on 2026-09-21; the aggregate's two seeded re-runs (batches 11 and 148) on the pod", "note": "The exclusion of every rank-5 decomposition of |H>^6 lives in the 190 stored batch outputs under research/h6_rank5/results/ (15 stage A batches over the 5,939,465 full 5-covers of |H>^3 with distinct independent base states, 158 stage B batches over the 12,390 dependent covers, 17 stage C batches over the 13,852 covers with a repeated state), each matching its covers at the four base points and re-deciding every candidate mod 2013265921 and numerically. The certificate checks the partition against the enumerator, re-enumerates the degenerate covers, verifies the hashes and geometry of every output, re-decides every stored hit, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/h6_rank5/batch.py, which regenerates any batch (`batch.py K`, 73.4 CPU-hours for all 190 on the pod: stage A 2.8, stage B 69.6, stage C 1.0).", "total": 180 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=6 certificate, which this cell re-runs" } }, { "slug": "qubit_H-m7-upper-9", "file": "bounds/qubit_H-m7-upper-9.json", "orbit": "qubit_H", "m": 7, "direction": "upper", "rank": 9, "tier": "lean", "ok": true, "date": "2022-02-18", "author": "Kissinger, van de Wetering, and Vilmart", "reference": "arXiv:2202.09202", "method": "literature", "pull_request": 83, "merge_commit": "e02f55453136aaba1d76fefb222c48eb29eb4ac9", "merge_date": "2026-09-21", "added_commit": "7b14437ef9eafdc34c2c5d3af161bff419a8e6b2", "added_date": "2026-09-21", "added_subject": "Add the Kissinger, van de Wetering, and Vilmart cells for qubit_H at m = 7, 8, 10", "receipt": "certs/qubit_H-m7-upper-9.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.QubitHM7StabRank", "lean_theorem": "qubit_h_m7_stabRankP_le_nine", "lean_receipt": "certs/lean-LeanProofs-QubitHM7StabRank.json", "lean_receipt_ok": true, "compute": { "cpu_hours": 0.01, "wall_clock_hours": 0.01, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "qubit_H-m8-lower-6", "file": "bounds/qubit_H-m8-lower-6.json", "orbit": "qubit_H", "m": 8, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-09-22", "author": "this repository", "reference": "stabrank research/h6_rank5", "method": "projection monotonicity applied to the attested exact rank-5 exclusion at m=6", "pull_request": 102, "merge_commit": "940bbc3f5061af0b0c86aad7f5debc49e77ae683", "merge_date": "2026-09-22", "added_commit": "c7155b380cbd0232d30d52f8eeeb2c131536964c", "added_date": "2026-09-22", "added_subject": "Project chi(H^6) >= 6 to the m = 7, 8, and 10 cells at the attested tier", "receipt": "certs/qubit_H-m8-lower-6.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_h_m6_rank5_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/h6_rank5/batch_manifest.json", "recomputed": 2, "compute_hours": 73.4, "hardware": "187 batches on a RunPod CPU pod (16 vCPU AMD EPYC 4564P, shared host at load 30 to 45, ten batches in parallel, nice 19), 2026-09-22 01:37 to 08:31 UTC; batches 14, 15, and 173 on an Apple silicon laptop (one core, nice 19) during the pipeline test on 2026-09-21; the aggregate's two seeded re-runs (batches 11 and 148) on the pod", "note": "The exclusion of every rank-5 decomposition of |H>^6 lives in the 190 stored batch outputs under research/h6_rank5/results/ (15 stage A batches over the 5,939,465 full 5-covers of |H>^3 with distinct independent base states, 158 stage B batches over the 12,390 dependent covers, 17 stage C batches over the 13,852 covers with a repeated state), each matching its covers at the four base points and re-deciding every candidate mod 2013265921 and numerically. The certificate checks the partition against the enumerator, re-enumerates the degenerate covers, verifies the hashes and geometry of every output, re-decides every stored hit, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/h6_rank5/batch.py, which regenerates any batch (`batch.py K`, 73.4 CPU-hours for all 190 on the pod: stage A 2.8, stage B 69.6, stage C 1.0).", "total": 180 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=6 certificate, which this cell re-runs" } }, { "slug": "qubit_H-m8-upper-12", "file": "bounds/qubit_H-m8-upper-12.json", "orbit": "qubit_H", "m": 8, "direction": "upper", "rank": 12, "tier": "lean", "ok": true, "date": "2022-02-18", "author": "Kissinger, van de Wetering, and Vilmart", "reference": "arXiv:2202.09202", "method": "literature", "pull_request": 83, "merge_commit": "e02f55453136aaba1d76fefb222c48eb29eb4ac9", "merge_date": "2026-09-21", "added_commit": "7b14437ef9eafdc34c2c5d3af161bff419a8e6b2", "added_date": "2026-09-21", "added_subject": "Add the Kissinger, van de Wetering, and Vilmart cells for qubit_H at m = 7, 8, 10", "receipt": "certs/qubit_H-m8-upper-12.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.QubitHM8StabRank", "lean_theorem": "qubit_h_m8_stabRankP_le_twelve", "lean_receipt": "certs/lean-LeanProofs-QubitHM8StabRank.json", "lean_receipt_ok": true, "compute": { "cpu_hours": 0.01, "wall_clock_hours": 0.01, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "qubit_H-m9-lower-6", "file": "bounds/qubit_H-m9-lower-6.json", "orbit": "qubit_H", "m": 9, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank research/h6_rank5", "method": "projection monotonicity applied to the attested exact rank-5 exclusion at m=6", "pull_request": 183, "merge_commit": "e83c42477b7b5caacc210c1e27aa42652a6aa829", "merge_date": "2026-10-21", "added_commit": "182cf4a188175344c30d47e268d8f67ce5551521", "added_date": "2026-10-21", "added_subject": "Carry the qubit_H lower bound to m = 9 by projection monotonicity", "receipt": "certs/qubit_H-m9-lower-6.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_qubit_h_m6_rank5_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/h6_rank5/batch_manifest.json", "recomputed": 2, "compute_hours": 73.4, "hardware": "187 batches on a RunPod CPU pod (16 vCPU AMD EPYC 4564P, shared host at load 30 to 45, ten batches in parallel, nice 19), 2026-09-22 01:37 to 08:31 UTC; batches 14, 15, and 173 on an Apple silicon laptop (one core, nice 19) during the pipeline test on 2026-09-21; the aggregate's two seeded re-runs (batches 11 and 148) on the pod", "note": "The exclusion of every rank-5 decomposition of |H>^6 lives in the 190 stored batch outputs under research/h6_rank5/results/ (15 stage A batches over the 5,939,465 full 5-covers of |H>^3 with distinct independent base states, 158 stage B batches over the 12,390 dependent covers, 17 stage C batches over the 13,852 covers with a repeated state), each matching its covers at the four base points and re-deciding every candidate mod 2013265921 and numerically. The certificate checks the partition against the enumerator, re-enumerates the degenerate covers, verifies the hashes and geometry of every output, re-decides every stored hit, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/h6_rank5/batch.py, which regenerates any batch (`batch.py K`, 73.4 CPU-hours for all 190 on the pod: stage A 2.8, stage B 69.6, stage C 1.0).", "total": 180 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=6 certificate, which this cell re-runs" } }, { "slug": "qubit_H-m9-upper-18", "file": "bounds/qubit_H-m9-upper-18.json", "orbit": "qubit_H", "m": 9, "direction": "upper", "rank": 18, "tier": "verified", "ok": true, "date": "2026-09-22", "author": "this repository", "reference": "arXiv:2106.07740, arXiv:2202.09202", "method": "structured construction", "pull_request": 104, "merge_commit": "9ce1755563ec6c7baf82903aae865f48b7668a45", "merge_date": "2026-09-22", "added_commit": "d47094a8e5a3ceb61d5905589705a08f4a9d48c8", "added_date": "2026-09-22", "added_subject": "Sweep of 2026-09-22: five product and cat witnesses, T3 sector contraction, literature update", "receipt": "certs/qubit_H-m9-upper-18.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.01, "wall_clock_hours": 0.01, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "qubit_T-m1-lower-2", "file": "bounds/qubit_T-m1-lower-2.json", "orbit": "qubit_T", "m": 1, "direction": "lower", "rank": 2, "tier": "verified", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank verify_challenge", "method": "exact: the state is not a stabilizer state (the moduli cos(beta) and sin(beta), cos(2 beta) = 1/sqrt3, differ)", "pull_request": 177, "merge_commit": "2fffdf2d28dafba398e4162820f9df00b1eefefb", "merge_date": "2026-10-21", "added_commit": "dd232c348dfd99d3339e2e11dcad6749b7bc27e9", "added_date": "2026-10-21", "added_subject": "File the single-copy cells of H3, N, qubit_H, and qubit_T", "receipt": "certs/qubit_T-m1-lower-2.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_rank1_moduli.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": null }, { "slug": "qubit_T-m1-upper-2", "file": "bounds/qubit_T-m1-upper-2.json", "orbit": "qubit_T", "m": 1, "direction": "upper", "rank": 2, "tier": "verified", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank research/constructions/data", "method": "direct construction: the single-copy state as a combination of two stabilizer states", "pull_request": 177, "merge_commit": "2fffdf2d28dafba398e4162820f9df00b1eefefb", "merge_date": "2026-10-21", "added_commit": "dd232c348dfd99d3339e2e11dcad6749b7bc27e9", "added_date": "2026-10-21", "added_subject": "File the single-copy cells of H3, N, qubit_H, and qubit_T", "receipt": "certs/qubit_T-m1-upper-2.json", "receipt_matches": true, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "qubit_T-m10-lower-6", "file": "bounds/qubit_T-m10-lower-6.json", "orbit": "qubit_T", "m": 10, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank research/t5_rank5", "method": "projection monotonicity applied to the attested exact rank-5 exclusion at m=5", "pull_request": 184, "merge_commit": "5597aeb6bc6b281b80dc827bbc9ff4b2f2496516", "merge_date": "2026-10-21", "added_commit": "27a27e763449088f5a60e2513f7840108935e8a4", "added_date": "2026-10-21", "added_subject": "Carry the qubit_T lower bound to m = 7 to 10 by projection monotonicity", "receipt": "certs/qubit_T-m10-lower-6.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_qubit_t_m5_rank5_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/t5_rank5/batch_manifest.json", "recomputed": 2, "compute_hours": 36.4, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host (load 30 to 40), fifteen batches in parallel at nice 19, 2026-09-24 07:37 to 10:04 UTC (the gamma smoke batch 159 at 07:37, the 160-batch loop 07:40 to 10:04); the aggregate's two seeded re-runs (batches 10 and 58) on the same pod at 10:05 UTC", "note": "The exclusion of every rank-5 decomposition of |T>^5 lives in the stored batch outputs under research/t5_rank5/results/ (the full 5-covers, 4-covers and 3-covers of |T>^3 up to symmetry, each matched at the base point 00 along qubits 1, 2 with the invisible terms on every flat missing 00 and every candidate re-decided mod 2013265921 and numerically): 0 hits, 0 refused, 0 undecided. The certificate re-enumerates the lists, verifies the hashes and geometry of every output, re-decides every stored hit, fails on any refusal or undecided run, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/t5_rank5/batch.py, which regenerates any batch (batch.py K).", "total": 160 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=5 certificate, which this cell re-runs" } }, { "slug": "qubit_T-m10-upper-15", "file": "bounds/qubit_T-m10-upper-15.json", "orbit": "qubit_T", "m": 10, "direction": "upper", "rank": 15, "tier": "verified", "ok": true, "date": "2026-10-12", "author": "Samuel Bevins", "reference": "arxiv:2610.17500", "method": "structured construction from a fifteen-word identity", "pull_request": 163, "merge_commit": "aaff4fc481b5b5b789cbdc96c7c92f7648d63989", "merge_date": "2026-10-15", "added_commit": "eb02bf3e56a941ef4d3c39b3bd3b1c4e3ea26fc7", "added_date": "2026-10-12", "added_subject": "qubit_T m=10: chi <= 15 (gamma 0.3907)", "receipt": "certs/qubit_T-m10-upper-15.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "direct construction, no search" } }, { "slug": "qubit_T-m10-upper-18", "file": "bounds/qubit_T-m10-upper-18.json", "orbit": "qubit_T", "m": 10, "direction": "upper", "rank": 18, "tier": "verified", "ok": true, "date": "2026-09-22", "author": "this repository", "reference": "stabrank research/constructions/product_witness.py", "method": "structured construction", "pull_request": 104, "merge_commit": "9ce1755563ec6c7baf82903aae865f48b7668a45", "merge_date": "2026-09-22", "added_commit": "d47094a8e5a3ceb61d5905589705a08f4a9d48c8", "added_date": "2026-09-22", "added_subject": "Sweep of 2026-09-22: five product and cat witnesses, T3 sector contraction, literature update", "receipt": "certs/qubit_T-m10-upper-18.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "qubit_T-m2-lower-2", "file": "bounds/qubit_T-m2-lower-2.json", "orbit": "qubit_T", "m": 2, "direction": "lower", "rank": 2, "tier": "lean", "ok": true, "date": "2026-09-20", "author": "this repository", "reference": "stabrank verify_challenge", "method": "exact: the state is not a stabilizer state (two distinct amplitude moduli)", "pull_request": 61, "merge_commit": "fec578fb6ad236de4564d49145a619b4924bd963", "merge_date": "2026-09-20", "added_commit": "801680d49c63f74d82974b5bab3f9b566965b959", "added_date": "2026-09-20", "added_subject": "Lower bounds for the five cells that had none", "receipt": "certs/qubit_T-m2-lower-2.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_rank1_moduli.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.QubitM2Lower", "lean_theorem": "qubit_t_m2_stabRankP_gt_one", "lean_receipt": "certs/lean-LeanProofs-QubitM2Lower.json", "lean_receipt_ok": true, "compute": null }, { "slug": "qubit_T-m2-upper-2", "file": "bounds/qubit_T-m2-upper-2.json", "orbit": "qubit_T", "m": 2, "direction": "upper", "rank": 2, "tier": "lean", "ok": true, "date": "2026-09-16", "author": "this repository", "reference": "stabrank annealer", "method": "simulated annealing over stabilizer states, then exact refit", "pull_request": 23, "merge_commit": "4ef357db2e821e5d4c5d518d2895a59288cdb85f", "merge_date": "2026-09-17", "added_commit": "c1a03fe3f58032297193e88fcb709a5a7facebea", "added_date": "2026-09-16", "added_subject": "Give every cited upper bound a verified witness, and correct qubit_H at m=6", "receipt": "certs/qubit_T-m2-upper-2.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.QubitTStabRank", "lean_theorem": "qubit_t_m2_stabRankP_le_two", "lean_receipt": "certs/lean-LeanProofs-QubitTStabRank.json", "lean_receipt_ok": true, "compute": { "cpu_hours": 0.01, "wall_clock_hours": 0.01, "runs": 1, "hardware": "Apple silicon laptop, 8 annealing chains" } }, { "slug": "qubit_T-m3-lower-3", "file": "bounds/qubit_T-m3-lower-3.json", "orbit": "qubit_T", "m": 3, "direction": "lower", "rank": 3, "tier": "reproduced", "ok": true, "date": "2026-09-16", "author": "this repository", "reference": "stabrank rank_exclusion.py", "method": "exhaustion over all pairs of 3-qubit stabilizer states, via the quotient by the target", "pull_request": 24, "merge_commit": "7e72a78cefefa660acca809d2c7275424fb32258", "merge_date": "2026-09-17", "added_commit": "19fd51cfa2a46b7c8c818baefa784842d97b07d7", "added_date": "2026-09-16", "added_subject": "Certify nine lower bounds: five cells settled, T3 at m=4 bounded for the first time", "receipt": "certs/qubit_T-m3-lower-3.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_t_m3_rank2.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop" } }, { "slug": "qubit_T-m3-upper-3", "file": "bounds/qubit_T-m3-upper-3.json", "orbit": "qubit_T", "m": 3, "direction": "upper", "rank": 3, "tier": "lean", "ok": true, "date": "2026-09-16", "author": "this repository", "reference": "stabrank annealer", "method": "simulated annealing over stabilizer states, then exact refit", "pull_request": 23, "merge_commit": "4ef357db2e821e5d4c5d518d2895a59288cdb85f", "merge_date": "2026-09-17", "added_commit": "c1a03fe3f58032297193e88fcb709a5a7facebea", "added_date": "2026-09-16", "added_subject": "Give every cited upper bound a verified witness, and correct qubit_H at m=6", "receipt": "certs/qubit_T-m3-upper-3.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.QubitTStabRank", "lean_theorem": "qubit_t_m3_stabRankP_le_three", "lean_receipt": "certs/lean-LeanProofs-QubitTStabRank.json", "lean_receipt_ok": true, "compute": { "cpu_hours": 0.01, "wall_clock_hours": 0.01, "runs": 1, "hardware": "Apple silicon laptop, 8 annealing chains" } }, { "slug": "qubit_T-m4-lower-3", "file": "bounds/qubit_T-m4-lower-3.json", "orbit": "qubit_T", "m": 4, "direction": "lower", "rank": 3, "tier": "reproduced", "ok": true, "date": "2026-09-12", "author": "this repository", "reference": "stabrank PR #18", "method": "exhaustion over all pairs of stabilizer states, via the quotient by the target", "pull_request": 18, "merge_commit": "293f15c35bdf189751f6e2b8cf833f535d04f287", "merge_date": "2026-09-16", "added_commit": "2fad4bd18188a4f950ae84661a03ffa307f7eca5", "added_date": "2026-09-12", "added_subject": "Close the qubit rank-2 cells too", "receipt": "certs/qubit_T-m4-lower-3.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_rank2.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": null }, { "slug": "qubit_T-m4-upper-3", "file": "bounds/qubit_T-m4-upper-3.json", "orbit": "qubit_T", "m": 4, "direction": "upper", "rank": 3, "tier": "lean", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": null, "receipt_matches": null, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.QubitTM4StabRank", "lean_theorem": "qubit_t_m4_stabRankP_le_three", "lean_receipt": "certs/lean-LeanProofs-QubitTM4StabRank.json", "lean_receipt_ok": true, "compute": null }, { "slug": "qubit_T-m5-lower-3", "file": "bounds/qubit_T-m5-lower-3.json", "orbit": "qubit_T", "m": 5, "direction": "lower", "rank": 3, "tier": "reproduced", "ok": true, "date": "2026-09-18", "author": "this repository", "reference": "stabrank rank_exclusion.py", "method": "projection monotonicity applied to an exhaustive exclusion at lower m", "pull_request": 37, "merge_commit": "8123be156aa8ee0394af17b6cc170fdbff894af3", "merge_date": "2026-09-18", "added_commit": "be6917e6b0b390196a355d6051beb3197ef043d7", "added_date": "2026-09-18", "added_subject": "Fill the S and BK T-type cells at m=5, both directions", "receipt": "certs/qubit_T-m5-lower-3.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_t_m5_from_m4.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.01, "wall_clock_hours": 0.005, "runs": 1, "hardware": "Apple silicon laptop" } }, { "slug": "qubit_T-m5-lower-4", "file": "bounds/qubit_T-m5-lower-4.json", "orbit": "qubit_T", "m": 5, "direction": "lower", "rank": 4, "tier": "reproduced", "ok": true, "date": "2026-09-18", "author": "this repository", "reference": "stabrank slice_lift.py", "method": "slice-and-lift: every rank-3 decomposition of |T>^4 up to symmetry, none extends to |T>^5", "pull_request": 39, "merge_commit": "7daa655cb357eb2c1ce802442b28ba2a49f74c43", "merge_date": "2026-09-18", "added_commit": "f85b915cc11f16fd851aadd7e282e35e4232063f", "added_date": "2026-09-18", "added_subject": "chi(T^5) >= 4 by slice-and-lift", "receipt": "certs/qubit_T-m5-lower-4.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_t_m5_lift.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.01, "wall_clock_hours": 0.005, "runs": 1, "hardware": "Apple silicon laptop" } }, { "slug": "qubit_T-m5-lower-5", "file": "bounds/qubit_T-m5-lower-5.json", "orbit": "qubit_T", "m": 5, "direction": "lower", "rank": 5, "tier": "attested", "ok": true, "date": "2026-09-24", "author": "this repository", "reference": "stabrank research/t5_rank4", "method": "two-qubit base slice: every rank-4 decomposition of |T>^5 has, along qubits 1, 2 at a base point in {00, 01}, all four terms visible, so its base is a full 4-cover of |T>^3; every such cover is completed slice by slice under the slice structure lemma, modulo 65521 over Q(zeta_24) with exact re-decision", "pull_request": 127, "merge_commit": "bf2bd2f567b6a4dcb12affd77f22c08c624307e0", "merge_date": "2026-09-23", "added_commit": "ad89d8623f947b213ac5a4279e0c4daf6a0baca4", "added_date": "2026-09-23", "added_subject": "chi(T^5) >= 5 and chi(T^6) >= 5: the attested bounds from the rank-4 exclusion", "receipt": "certs/qubit_T-m5-lower-5.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_t_m5_rank4_attested.py", "certificate_budget_s": 1800, "certificate_attested": { "batches": "research/t5_rank4/batch_manifest.json", "recomputed": 2, "compute_hours": 0.002, "hardware": "Apple M5 Pro laptop (macOS 26.5.1), one core at nice 19 under load from other sessions, 2026-09-24 02:25 UTC; the aggregate's two seeded re-runs (batches 0 and 1) on the same machine at 02:26 UTC", "note": "The exclusion of every rank-4 decomposition of |T>^5 lives in the stored batch outputs under research/t5_rank4/results/ (partition.json over the census covers4.json: the 4,709 full 4-covers of |T>^3 up to the unitary symmetry of |T>^3, 4,697 of distinct independent states and 12 with a repeated state, each matched at the base points 00 and 01 along qubits 1, 2 with every candidate re-decided mod 2013265921 and numerically): 0 hits, 0 refused, 0 undecided. The certificate re-enumerates the census, verifies the hashes and geometry of every output, re-decides every stored hit, fails on any refusal or undecided run, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/t5_rank4/batch.py, which regenerates any batch (batch.py K).", "total": 6 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.002, "wall_clock_hours": 0.002, "runs": 1, "hardware": "Apple M5 Pro laptop (macOS 26.5.1), one core at nice 19 under load from other sessions, 2026-09-24 02:25 UTC; the aggregate's two seeded re-runs (batches 0 and 1) on the same machine at 02:26 UTC" } }, { "slug": "qubit_T-m5-lower-6", "file": "bounds/qubit_T-m5-lower-6.json", "orbit": "qubit_T", "m": 5, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-09-24", "author": "this repository", "reference": "stabrank research/t5_rank5", "method": "two-qubit base slice at 00: every rank-5 decomposition of |T>^5 has three, four or five terms visible at 00 along qubits 1, 2 (chi(T^3) = 3), so its base is a full 3-, 4- or 5-cover of |T>^3 and the invisible terms lie on the six flats missing 00; every base is completed slice by slice under the slice structure lemma for every flat choice, modulo 65521 over Q(zeta_24) with exact re-decision", "pull_request": 132, "merge_commit": "385fd48af6aee9cebb524faa3254799d619a8499", "merge_date": "2026-09-24", "added_commit": "a10a9e6e6b116436a06da7bf690d032400e47ca1", "added_date": "2026-09-24", "added_subject": "chi(T^5) >= 6 and chi(T^6) >= 6: the rank-5 exclusion run, its batch manifest, and the attested bounds", "receipt": "certs/qubit_T-m5-lower-6.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_t_m5_rank5_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/t5_rank5/batch_manifest.json", "recomputed": 2, "compute_hours": 36.4, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host (load 30 to 40), fifteen batches in parallel at nice 19, 2026-09-24 07:37 to 10:04 UTC (the gamma smoke batch 159 at 07:37, the 160-batch loop 07:40 to 10:04); the aggregate's two seeded re-runs (batches 10 and 58) on the same pod at 10:05 UTC", "note": "The exclusion of every rank-5 decomposition of |T>^5 lives in the stored batch outputs under research/t5_rank5/results/ (partition.json: stage A batches over the 6,115,136 full 5-covers of |T>^3 with distinct independent base states, stage B batches over the 20,653 dependent covers, stage C batches over the 23,120 covers with a repeated state, the 4,308 cancel-at-base multisets included, stage beta batches over the 4,709 full 4-covers, each with the invisible term on every one of the six flats missing 00, and one stage gamma batch over the 4 full 3-covers with every one of the 21 flat pairs), every base matched at the base point 00 along qubits 1, 2 and every candidate re-decided mod 2013265921 and numerically: 0 hits, 0 refused, 0 undecided. The certificate checks the partition against the enumerator and the census hash, re-enumerates the 3-covers, the 4-covers and the degenerate 5-multisets, verifies the hashes and geometry of every output, re-decides every stored hit, fails on any refusal or undecided run, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/t5_rank5/batch.py, which regenerates any batch (batch.py K).", "total": 160 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 36.4, "wall_clock_hours": 2.5, "runs": 1, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host (load 30 to 40), fifteen batches in parallel at nice 19, 2026-09-24 07:37 to 10:04 UTC (the gamma smoke batch 159 at 07:37, the 160-batch loop 07:40 to 10:04); the aggregate's two seeded re-runs (batches 10 and 58) on the same pod at 10:05 UTC" } }, { "slug": "qubit_T-m5-upper-6", "file": "bounds/qubit_T-m5-upper-6.json", "orbit": "qubit_T", "m": 5, "direction": "upper", "rank": 6, "tier": "lean", "ok": true, "date": "2026-09-18", "author": "this repository", "reference": "product of board witnesses", "method": "tensor product of verified lower-m witnesses", "pull_request": 37, "merge_commit": "8123be156aa8ee0394af17b6cc170fdbff894af3", "merge_date": "2026-09-18", "added_commit": "be6917e6b0b390196a355d6051beb3197ef043d7", "added_date": "2026-09-18", "added_subject": "Fill the S and BK T-type cells at m=5, both directions", "receipt": "certs/qubit_T-m5-upper-6.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.QubitTM5StabRank", "lean_theorem": "qubit_t_m5_stabRankP_le_six", "lean_receipt": "certs/lean-LeanProofs-QubitTM5StabRank.json", "lean_receipt_ok": true, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop" } }, { "slug": "qubit_T-m6-lower-4", "file": "bounds/qubit_T-m6-lower-4.json", "orbit": "qubit_T", "m": 6, "direction": "lower", "rank": 4, "tier": "reproduced", "ok": true, "date": "2026-09-20", "author": "this repository", "reference": "stabrank verify_challenge", "method": "projection monotonicity applied to the slice-and-lift bound at m=5", "pull_request": 61, "merge_commit": "fec578fb6ad236de4564d49145a619b4924bd963", "merge_date": "2026-09-20", "added_commit": "801680d49c63f74d82974b5bab3f9b566965b959", "added_date": "2026-09-20", "added_subject": "Lower bounds for the five cells that had none", "receipt": "certs/qubit_T-m6-lower-4.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_t_m5_lift.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.01, "wall_clock_hours": 0.003, "runs": 1, "hardware": "the m=5 certificate" } }, { "slug": "qubit_T-m6-lower-5", "file": "bounds/qubit_T-m6-lower-5.json", "orbit": "qubit_T", "m": 6, "direction": "lower", "rank": 5, "tier": "attested", "ok": true, "date": "2026-09-24", "author": "this repository", "reference": "stabrank research/t5_rank4", "method": "projection monotonicity applied to the attested exact rank-4 exclusion at m=5", "pull_request": 127, "merge_commit": "bf2bd2f567b6a4dcb12affd77f22c08c624307e0", "merge_date": "2026-09-23", "added_commit": "ad89d8623f947b213ac5a4279e0c4daf6a0baca4", "added_date": "2026-09-23", "added_subject": "chi(T^5) >= 5 and chi(T^6) >= 5: the attested bounds from the rank-4 exclusion", "receipt": "certs/qubit_T-m6-lower-5.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_t_m5_rank4_attested.py", "certificate_budget_s": 1800, "certificate_attested": { "batches": "research/t5_rank4/batch_manifest.json", "recomputed": 2, "compute_hours": 0.002, "hardware": "Apple M5 Pro laptop (macOS 26.5.1), one core at nice 19 under load from other sessions, 2026-09-24 02:25 UTC; the aggregate's two seeded re-runs (batches 0 and 1) on the same machine at 02:26 UTC", "note": "The exclusion of every rank-4 decomposition of |T>^5 lives in the 6 stored batch outputs under research/t5_rank4/results/ (the 4,709 full 4-covers of |T>^3 up to symmetry, each matched at the base points 00 and 01 along qubits 1, 2 with every candidate re-decided mod 2013265921 and numerically): 0 hits, 0 refused, 0 undecided. The certificate re-enumerates the census, verifies the hashes and geometry of every output, re-decides every stored hit, fails on any refusal or undecided run, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/t5_rank4/batch.py, which regenerates any batch (batch.py K).", "total": 6 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=5 certificate, which this cell re-runs" } }, { "slug": "qubit_T-m6-lower-6", "file": "bounds/qubit_T-m6-lower-6.json", "orbit": "qubit_T", "m": 6, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-09-24", "author": "this repository", "reference": "stabrank research/t5_rank5", "method": "projection monotonicity applied to the attested exact rank-5 exclusion at m=5", "pull_request": 132, "merge_commit": "385fd48af6aee9cebb524faa3254799d619a8499", "merge_date": "2026-09-24", "added_commit": "a10a9e6e6b116436a06da7bf690d032400e47ca1", "added_date": "2026-09-24", "added_subject": "chi(T^5) >= 6 and chi(T^6) >= 6: the rank-5 exclusion run, its batch manifest, and the attested bounds", "receipt": "certs/qubit_T-m6-lower-6.json", "receipt_matches": false, "certificate_script": "verify_challenge/cert_qubit_t_m5_rank5_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/t5_rank5/batch_manifest.json", "recomputed": 2, "compute_hours": 36.4, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host (load 30 to 40), fifteen batches in parallel at nice 19, 2026-09-24 07:37 to 10:04 UTC (the gamma smoke batch 159 at 07:37, the 160-batch loop 07:40 to 10:04); the aggregate's two seeded re-runs (batches 10 and 58) on the same pod at 10:05 UTC", "note": "The exclusion of every rank-5 decomposition of |T>^5 lives in the stored batch outputs under research/t5_rank5/results/ (the full 5-covers, 4-covers and 3-covers of |T>^3 up to symmetry, each matched at the base point 00 along qubits 1, 2 with the invisible terms on every flat missing 00 and every candidate re-decided mod 2013265921 and numerically): 0 hits, 0 refused, 0 undecided. The certificate re-enumerates the lists, verifies the hashes and geometry of every output, re-decides every stored hit, fails on any refusal or undecided run, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/t5_rank5/batch.py, which regenerates any batch (batch.py K).", "total": 160 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=5 certificate, which this cell re-runs" } }, { "slug": "qubit_T-m6-upper-6", "file": "bounds/qubit_T-m6-upper-6.json", "orbit": "qubit_T", "m": 6, "direction": "upper", "rank": 6, "tier": "lean", "ok": true, "date": "2026-05-27", "author": "Labib and Russo", "reference": "arXiv:2605.28586", "method": "literature", "pull_request": 17, "merge_commit": "c856eab447ebbf179276a4e34ef7c36752398069", "merge_date": "2026-09-12", "added_commit": "21f53b5a0e410cfa6de8e7c4bea2cd906884bd33", "added_date": "2026-09-12", "added_subject": "Add a verified-submission leaderboard for stabilizer-rank bounds", "receipt": "certs/qubit_T-m6-upper-6.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": "LeanProofs.QubitTM6StabRank", "lean_theorem": "qubit_t_m6_stabRankP_le_six", "lean_receipt": "certs/lean-LeanProofs-QubitTM6StabRank.json", "lean_receipt_ok": true, "compute": null }, { "slug": "qubit_T-m7-lower-6", "file": "bounds/qubit_T-m7-lower-6.json", "orbit": "qubit_T", "m": 7, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank research/t5_rank5", "method": "projection monotonicity applied to the attested exact rank-5 exclusion at m=5", "pull_request": 184, "merge_commit": "5597aeb6bc6b281b80dc827bbc9ff4b2f2496516", "merge_date": "2026-10-21", "added_commit": "27a27e763449088f5a60e2513f7840108935e8a4", "added_date": "2026-10-21", "added_subject": "Carry the qubit_T lower bound to m = 7 to 10 by projection monotonicity", "receipt": "certs/qubit_T-m7-lower-6.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_qubit_t_m5_rank5_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/t5_rank5/batch_manifest.json", "recomputed": 2, "compute_hours": 36.4, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host (load 30 to 40), fifteen batches in parallel at nice 19, 2026-09-24 07:37 to 10:04 UTC (the gamma smoke batch 159 at 07:37, the 160-batch loop 07:40 to 10:04); the aggregate's two seeded re-runs (batches 10 and 58) on the same pod at 10:05 UTC", "note": "The exclusion of every rank-5 decomposition of |T>^5 lives in the stored batch outputs under research/t5_rank5/results/ (the full 5-covers, 4-covers and 3-covers of |T>^3 up to symmetry, each matched at the base point 00 along qubits 1, 2 with the invisible terms on every flat missing 00 and every candidate re-decided mod 2013265921 and numerically): 0 hits, 0 refused, 0 undecided. The certificate re-enumerates the lists, verifies the hashes and geometry of every output, re-decides every stored hit, fails on any refusal or undecided run, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/t5_rank5/batch.py, which regenerates any batch (batch.py K).", "total": 160 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=5 certificate, which this cell re-runs" } }, { "slug": "qubit_T-m7-upper-9", "file": "bounds/qubit_T-m7-upper-9.json", "orbit": "qubit_T", "m": 7, "direction": "upper", "rank": 9, "tier": "verified", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank research/constructions/product_witness.py", "method": "structured construction", "pull_request": 177, "merge_commit": "2fffdf2d28dafba398e4162820f9df00b1eefefb", "merge_date": "2026-10-21", "added_commit": "c302c75c9cff516798e7801a592df0583adf918f", "added_date": "2026-10-21", "added_subject": "Fill the qubit T-type cells at seven and nine copies with derived witnesses", "receipt": "certs/qubit_T-m7-upper-9.json", "receipt_matches": true, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "qubit_T-m8-lower-6", "file": "bounds/qubit_T-m8-lower-6.json", "orbit": "qubit_T", "m": 8, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank research/t5_rank5", "method": "projection monotonicity applied to the attested exact rank-5 exclusion at m=5", "pull_request": 184, "merge_commit": "5597aeb6bc6b281b80dc827bbc9ff4b2f2496516", "merge_date": "2026-10-21", "added_commit": "27a27e763449088f5a60e2513f7840108935e8a4", "added_date": "2026-10-21", "added_subject": "Carry the qubit_T lower bound to m = 7 to 10 by projection monotonicity", "receipt": "certs/qubit_T-m8-lower-6.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_qubit_t_m5_rank5_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/t5_rank5/batch_manifest.json", "recomputed": 2, "compute_hours": 36.4, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host (load 30 to 40), fifteen batches in parallel at nice 19, 2026-09-24 07:37 to 10:04 UTC (the gamma smoke batch 159 at 07:37, the 160-batch loop 07:40 to 10:04); the aggregate's two seeded re-runs (batches 10 and 58) on the same pod at 10:05 UTC", "note": "The exclusion of every rank-5 decomposition of |T>^5 lives in the stored batch outputs under research/t5_rank5/results/ (the full 5-covers, 4-covers and 3-covers of |T>^3 up to symmetry, each matched at the base point 00 along qubits 1, 2 with the invisible terms on every flat missing 00 and every candidate re-decided mod 2013265921 and numerically): 0 hits, 0 refused, 0 undecided. The certificate re-enumerates the lists, verifies the hashes and geometry of every output, re-decides every stored hit, fails on any refusal or undecided run, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/t5_rank5/batch.py, which regenerates any batch (batch.py K).", "total": 160 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=5 certificate, which this cell re-runs" } }, { "slug": "qubit_T-m8-upper-9", "file": "bounds/qubit_T-m8-upper-9.json", "orbit": "qubit_T", "m": 8, "direction": "upper", "rank": 9, "tier": "verified", "ok": true, "date": "2026-09-22", "author": "this repository", "reference": "stabrank research/constructions/product_witness.py", "method": "structured construction", "pull_request": 104, "merge_commit": "9ce1755563ec6c7baf82903aae865f48b7668a45", "merge_date": "2026-09-22", "added_commit": "d47094a8e5a3ceb61d5905589705a08f4a9d48c8", "added_date": "2026-09-22", "added_subject": "Sweep of 2026-09-22: five product and cat witnesses, T3 sector contraction, literature update", "receipt": "certs/qubit_T-m8-upper-9.json", "receipt_matches": false, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "qubit_T-m9-lower-6", "file": "bounds/qubit_T-m9-lower-6.json", "orbit": "qubit_T", "m": 9, "direction": "lower", "rank": 6, "tier": "attested", "ok": true, "date": "2026-10-17", "author": "this repository", "reference": "stabrank research/t5_rank5", "method": "projection monotonicity applied to the attested exact rank-5 exclusion at m=5", "pull_request": 184, "merge_commit": "5597aeb6bc6b281b80dc827bbc9ff4b2f2496516", "merge_date": "2026-10-21", "added_commit": "27a27e763449088f5a60e2513f7840108935e8a4", "added_date": "2026-10-21", "added_subject": "Carry the qubit_T lower bound to m = 7 to 10 by projection monotonicity", "receipt": "certs/qubit_T-m9-lower-6.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_qubit_t_m5_rank5_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/t5_rank5/batch_manifest.json", "recomputed": 2, "compute_hours": 36.4, "hardware": "RunPod CPU pod, 16 vCPU AMD EPYC 4564P on a shared host (load 30 to 40), fifteen batches in parallel at nice 19, 2026-09-24 07:37 to 10:04 UTC (the gamma smoke batch 159 at 07:37, the 160-batch loop 07:40 to 10:04); the aggregate's two seeded re-runs (batches 10 and 58) on the same pod at 10:05 UTC", "note": "The exclusion of every rank-5 decomposition of |T>^5 lives in the stored batch outputs under research/t5_rank5/results/ (the full 5-covers, 4-covers and 3-covers of |T>^3 up to symmetry, each matched at the base point 00 along qubits 1, 2 with the invisible terms on every flat missing 00 and every candidate re-decided mod 2013265921 and numerically): 0 hits, 0 refused, 0 undecided. The certificate re-enumerates the lists, verifies the hashes and geometry of every output, re-decides every stored hit, fails on any refusal or undecided run, and re-runs two batches from scratch; completeness rests on the stored outputs and on research/t5_rank5/batch.py, which regenerates any batch (batch.py K).", "total": 160 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m=5 certificate, which this cell re-runs" } }, { "slug": "qubit_T-m9-upper-15", "file": "bounds/qubit_T-m9-upper-15.json", "orbit": "qubit_T", "m": 9, "direction": "upper", "rank": 15, "tier": "verified", "ok": true, "date": "2026-10-18", "author": "this repository", "reference": "arxiv:2610.17500 (the m=10 identity) and stabrank bounds/qubit_T-m10-upper-15.json", "method": "projection of a verified witness", "pull_request": 177, "merge_commit": "2fffdf2d28dafba398e4162820f9df00b1eefefb", "merge_date": "2026-10-21", "added_commit": "c302c75c9cff516798e7801a592df0583adf918f", "added_date": "2026-10-21", "added_subject": "Fill the qubit T-type cells at seven and nine copies with derived witnesses", "receipt": "certs/qubit_T-m9-upper-15.json", "receipt_matches": true, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction from the m=10 witness, no search" } }, { "slug": "qubit_sqrtT-m1-lower-2", "file": "bounds/qubit_sqrtT-m1-lower-2.json", "orbit": "qubit_sqrtT", "m": 1, "direction": "lower", "rank": 2, "tier": "verified", "ok": true, "date": "2026-10-21", "author": "Vincent Russo", "reference": "stabrank verify_challenge", "method": "Galois descent over Z[i]: the four conjugates of the target under Gal(Q(zeta_16)/Q(i)) span a space of dimension min(4, m + 1); no search", "pull_request": 185, "merge_commit": "c0db0bc2173f75ddb06febaee85193b388e98b7d", "merge_date": "2026-10-21", "added_commit": "f544b5690471e06ef0801056ab0b66039b3d4776", "added_date": "2026-10-21", "added_subject": "Make sqrt(T) and CS board orbits with their first cells", "receipt": "certs/qubit_sqrtT-m1-lower-2.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_sqrtt_galois.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.003, "wall_clock_hours": 0.003, "runs": 1, "hardware": "Apple silicon laptop, one core; about 10 s for the certificate", "llm": [ { "model": "claude-fable-5-1", "role": "found the descent argument and wrote the certificate" } ] } }, { "slug": "qubit_sqrtT-m1-upper-2", "file": "bounds/qubit_sqrtT-m1-upper-2.json", "orbit": "qubit_sqrtT", "m": 1, "direction": "upper", "rank": 2, "tier": "verified", "ok": true, "date": "2026-10-17", "author": "Vincent Russo", "reference": "this repository (stabrank-research, round 31 new-orbit survey)", "method": "by hand: the computational basis, coefficients fitted exactly", "pull_request": 185, "merge_commit": "c0db0bc2173f75ddb06febaee85193b388e98b7d", "merge_date": "2026-10-21", "added_commit": "f544b5690471e06ef0801056ab0b66039b3d4776", "added_date": "2026-10-21", "added_subject": "Make sqrt(T) and CS board orbits with their first cells", "receipt": "certs/qubit_sqrtT-m1-upper-2.json", "receipt_matches": true, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "qubit_sqrtT-m2-lower-3", "file": "bounds/qubit_sqrtT-m2-lower-3.json", "orbit": "qubit_sqrtT", "m": 2, "direction": "lower", "rank": 3, "tier": "verified", "ok": true, "date": "2026-10-21", "author": "Vincent Russo", "reference": "stabrank verify_challenge", "method": "Galois descent over Z[i]: the four conjugates of the target under Gal(Q(zeta_16)/Q(i)) span a space of dimension min(4, m + 1); no search", "pull_request": 185, "merge_commit": "c0db0bc2173f75ddb06febaee85193b388e98b7d", "merge_date": "2026-10-21", "added_commit": "f544b5690471e06ef0801056ab0b66039b3d4776", "added_date": "2026-10-21", "added_subject": "Make sqrt(T) and CS board orbits with their first cells", "receipt": "certs/qubit_sqrtT-m2-lower-3.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_sqrtt_galois.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.003, "wall_clock_hours": 0.003, "runs": 1, "hardware": "Apple silicon laptop, one core; about 10 s for the certificate", "llm": [ { "model": "claude-fable-5-1", "role": "found the descent argument and wrote the certificate" } ] } }, { "slug": "qubit_sqrtT-m2-upper-3", "file": "bounds/qubit_sqrtT-m2-upper-3.json", "orbit": "qubit_sqrtT", "m": 2, "direction": "upper", "rank": 3, "tier": "verified", "ok": true, "date": "2026-10-17", "author": "Vincent Russo", "reference": "this repository (stabrank-research, round 31 new-orbit survey)", "method": "by hand: the symmetric-subspace basis |00>, |11>, (|01> + |10>)/sqrt 2, coefficients fitted exactly", "pull_request": 185, "merge_commit": "c0db0bc2173f75ddb06febaee85193b388e98b7d", "merge_date": "2026-10-21", "added_commit": "f544b5690471e06ef0801056ab0b66039b3d4776", "added_date": "2026-10-21", "added_subject": "Make sqrt(T) and CS board orbits with their first cells", "receipt": "certs/qubit_sqrtT-m2-upper-3.json", "receipt_matches": true, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "qubit_sqrtT-m3-lower-4", "file": "bounds/qubit_sqrtT-m3-lower-4.json", "orbit": "qubit_sqrtT", "m": 3, "direction": "lower", "rank": 4, "tier": "verified", "ok": true, "date": "2026-10-21", "author": "Vincent Russo", "reference": "stabrank verify_challenge", "method": "Galois descent over Z[i]: the four conjugates of the target under Gal(Q(zeta_16)/Q(i)) span a space of dimension min(4, m + 1); no search", "pull_request": 185, "merge_commit": "c0db0bc2173f75ddb06febaee85193b388e98b7d", "merge_date": "2026-10-21", "added_commit": "f544b5690471e06ef0801056ab0b66039b3d4776", "added_date": "2026-10-21", "added_subject": "Make sqrt(T) and CS board orbits with their first cells", "receipt": "certs/qubit_sqrtT-m3-lower-4.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_sqrtt_galois.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.003, "wall_clock_hours": 0.003, "runs": 1, "hardware": "Apple silicon laptop, one core; about 10 s for the certificate", "llm": [ { "model": "claude-fable-5-1", "role": "found the descent argument and wrote the certificate" } ] } }, { "slug": "qubit_sqrtT-m3-upper-4", "file": "bounds/qubit_sqrtT-m3-upper-4.json", "orbit": "qubit_sqrtT", "m": 3, "direction": "upper", "rank": 4, "tier": "verified", "ok": true, "date": "2026-10-17", "author": "Vincent Russo", "reference": "this repository (stabrank-research, round 31 new-orbit survey)", "method": "by hand: four product stabilizer states spanning Sym^3(C^2), coefficients fitted exactly in Q(zeta_16)", "pull_request": 185, "merge_commit": "c0db0bc2173f75ddb06febaee85193b388e98b7d", "merge_date": "2026-10-21", "added_commit": "f544b5690471e06ef0801056ab0b66039b3d4776", "added_date": "2026-10-21", "added_subject": "Make sqrt(T) and CS board orbits with their first cells", "receipt": "certs/qubit_sqrtT-m3-upper-4.json", "receipt_matches": true, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "qubit_sqrtT-m4-lower-4", "file": "bounds/qubit_sqrtT-m4-lower-4.json", "orbit": "qubit_sqrtT", "m": 4, "direction": "lower", "rank": 4, "tier": "verified", "ok": true, "date": "2026-10-21", "author": "Vincent Russo", "reference": "stabrank verify_challenge", "method": "Galois descent over Z[i]: the four conjugates of the target under Gal(Q(zeta_16)/Q(i)) span a space of dimension min(4, m + 1); no search", "pull_request": 185, "merge_commit": "c0db0bc2173f75ddb06febaee85193b388e98b7d", "merge_date": "2026-10-21", "added_commit": "f544b5690471e06ef0801056ab0b66039b3d4776", "added_date": "2026-10-21", "added_subject": "Make sqrt(T) and CS board orbits with their first cells", "receipt": "certs/qubit_sqrtT-m4-lower-4.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_sqrtt_galois.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.003, "wall_clock_hours": 0.003, "runs": 1, "hardware": "Apple silicon laptop, one core; about 10 s for the certificate", "llm": [ { "model": "claude-fable-5-1", "role": "found the descent argument and wrote the certificate" } ] } }, { "slug": "qubit_sqrtT-m4-lower-5", "file": "bounds/qubit_sqrtT-m4-lower-5.json", "orbit": "qubit_sqrtT", "m": 4, "direction": "lower", "rank": 5, "tier": "verified", "ok": true, "date": "2026-10-23", "author": "Vincent Russo", "reference": "this repository (stabrank-research, round 33)", "method": "exact census of the four-qubit stabilizer states inside the Galois-forced subspace V4: three states, of rank 3, so no four terms", "pull_request": 189, "merge_commit": "68e582eb026329fdea029935db0edc444c4792d2", "merge_date": "2026-10-24", "added_commit": "e2ff283573744c9c5195cfc69240298b45278563", "added_date": "2026-10-24", "added_subject": "sqrt(T): chi(R^4) = 5, chi(R^5) = 6, chi(R^6) >= 7 through the Galois-forced subspace (exact census and attested rank-6 census), and chi(R^7) <= 12 from the annealer", "receipt": "certs/qubit_sqrtT-m4-lower-5.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_sqrtt_galois_census.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.02, "wall_clock_hours": 0.01, "runs": 3, "hardware": "Apple silicon laptop (shared, load 70), three census runs of 25 s each at m = 4 and 5", "llm": [ { "model": "claude-fable-5-1", "role": "found the forced-subspace reduction, wrote the census and the certificate" } ] } }, { "slug": "qubit_sqrtT-m4-upper-5", "file": "bounds/qubit_sqrtT-m4-upper-5.json", "orbit": "qubit_sqrtT", "m": 4, "direction": "upper", "rank": 5, "tier": "verified", "ok": true, "date": "2026-10-17", "author": "Vincent Russo", "reference": "this repository (stabrank-research, round 31 new-orbit survey)", "method": "by hand: five product stabilizer states spanning Sym^4(C^2), coefficients fitted exactly in Q(zeta_16)", "pull_request": 185, "merge_commit": "c0db0bc2173f75ddb06febaee85193b388e98b7d", "merge_date": "2026-10-21", "added_commit": "f544b5690471e06ef0801056ab0b66039b3d4776", "added_date": "2026-10-21", "added_subject": "Make sqrt(T) and CS board orbits with their first cells", "receipt": "certs/qubit_sqrtT-m4-upper-5.json", "receipt_matches": true, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "qubit_sqrtT-m5-lower-6", "file": "bounds/qubit_sqrtT-m5-lower-6.json", "orbit": "qubit_sqrtT", "m": 5, "direction": "lower", "rank": 6, "tier": "verified", "ok": true, "date": "2026-10-23", "author": "Vincent Russo", "reference": "this repository (stabrank-research, round 33)", "method": "exact residue census of all 2,423,520 five-qubit stabilizer states modulo the Galois-forced subspace V4: no state inside V4 and no class of five with parallel residues", "pull_request": 189, "merge_commit": "68e582eb026329fdea029935db0edc444c4792d2", "merge_date": "2026-10-24", "added_commit": "e2ff283573744c9c5195cfc69240298b45278563", "added_date": "2026-10-24", "added_subject": "sqrt(T): chi(R^4) = 5, chi(R^5) = 6, chi(R^6) >= 7 through the Galois-forced subspace (exact census and attested rank-6 census), and chi(R^7) <= 12 from the annealer", "receipt": "certs/qubit_sqrtT-m5-lower-6.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_sqrtt_galois_census.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.02, "wall_clock_hours": 0.01, "runs": 3, "hardware": "Apple silicon laptop (shared, load 70), three census runs of 25 s each at m = 4 and 5", "llm": [ { "model": "claude-fable-5-1", "role": "found the forced-subspace reduction, wrote the census and the certificate" } ] } }, { "slug": "qubit_sqrtT-m5-upper-6", "file": "bounds/qubit_sqrtT-m5-upper-6.json", "orbit": "qubit_sqrtT", "m": 5, "direction": "upper", "rank": 6, "tier": "verified", "ok": true, "date": "2026-10-23", "author": "Vincent Russo", "reference": "this repository (stabrank-research, round 33)", "method": "by hand: the six product stabilizer states |0>^5, |1>^5, |+>^5, |->^5, |+i>^5, |-i>^5 span Sym^5(C^2); coefficients solved exactly in Q(zeta_16)", "pull_request": 189, "merge_commit": "68e582eb026329fdea029935db0edc444c4792d2", "merge_date": "2026-10-24", "added_commit": "e2ff283573744c9c5195cfc69240298b45278563", "added_date": "2026-10-24", "added_subject": "sqrt(T): chi(R^4) = 5, chi(R^5) = 6, chi(R^6) >= 7 through the Galois-forced subspace (exact census and attested rank-6 census), and chi(R^7) <= 12 from the annealer", "receipt": "certs/qubit_sqrtT-m5-upper-6.json", "receipt_matches": true, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "qubit_sqrtT-m6-lower-6", "file": "bounds/qubit_sqrtT-m6-lower-6.json", "orbit": "qubit_sqrtT", "m": 6, "direction": "lower", "rank": 6, "tier": "verified", "ok": true, "date": "2026-10-23", "author": "Vincent Russo", "reference": "this repository (stabrank-research, round 33)", "method": "projection monotonicity applied to the exact rank-5 exclusion at m=5", "pull_request": 189, "merge_commit": "68e582eb026329fdea029935db0edc444c4792d2", "merge_date": "2026-10-24", "added_commit": "e2ff283573744c9c5195cfc69240298b45278563", "added_date": "2026-10-24", "added_subject": "sqrt(T): chi(R^4) = 5, chi(R^5) = 6, chi(R^6) >= 7 through the Galois-forced subspace (exact census and attested rank-6 census), and chi(R^7) <= 12 from the annealer", "receipt": "certs/qubit_sqrtT-m6-lower-6.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_sqrtt_galois_census.py", "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.02, "wall_clock_hours": 0.01, "runs": 3, "hardware": "Apple silicon laptop (shared, load 70), three census runs of 25 s each at m = 4 and 5", "llm": [ { "model": "claude-fable-5-1", "role": "found the forced-subspace reduction, wrote the census and the certificate" } ] } }, { "slug": "qubit_sqrtT-m6-lower-7", "file": "bounds/qubit_sqrtT-m6-lower-7.json", "orbit": "qubit_sqrtT", "m": 6, "direction": "lower", "rank": 7, "tier": "attested", "ok": true, "date": "2026-10-23", "author": "Vincent Russo", "reference": "this repository (stabrank-research, round 33)", "method": "slice-and-lift from the complete rank-6 census of |sqrtT>^5 through the Galois-forced subspace: no six-term decomposition of |sqrtT>^5 lifts to six copies", "pull_request": 189, "merge_commit": "68e582eb026329fdea029935db0edc444c4792d2", "merge_date": "2026-10-24", "added_commit": "e2ff283573744c9c5195cfc69240298b45278563", "added_date": "2026-10-24", "added_subject": "sqrt(T): chi(R^4) = 5, chi(R^5) = 6, chi(R^6) >= 7 through the Galois-forced subspace (exact census and attested rank-6 census), and chi(R^7) <= 12 from the annealer", "receipt": "certs/qubit_sqrtT-m6-lower-7.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_sqrtt_m6_rank6_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/sqrtt_m5_rank6/batch_manifest.json", "recomputed": 2, "compute_hours": 46.3, "hardware": "Perlmutter CPU node (two AMD EPYC 7763, 128 worker processes), NERSC job 60159879, 2026-10-23 16:04 to 16:41 UTC; the representatives stage single-threaded (846 s), the pivot census 46.1 CPU-h over 128 workers (about 23 min wall)", "note": "The complete list of six-term stabilizer decompositions of |sqrtT>^5 lives in the stored batch outputs under research/sqrtt_m5_rank6/results/: for each of the 8,585 orbit representatives of the five-qubit stabilizer states under S_5 x , the residue classes modulo V4 + span(pivot) under two primes and every class that could carry a decomposition (one candidate set in all, the 18 symmetric states). The certificate re-enumerates the dictionary and checks its hash, verifies that the stored pivots meet every orbit exactly once, re-runs two blocks from scratch (seed printed) and compares them byte for byte, re-decides the candidate set exactly over Q(zeta_16) (3,375 decompositions, their exact coefficients), closes the list under the group, and runs the lift to six copies in full; completeness rests on the stored outputs and on research/sqrtt_m5_rank6/census.py, which regenerates any block (census.py run 5 OUT --pivots ...).", "total": 859 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 47.0, "wall_clock_hours": 0.7, "runs": 1, "hardware": "Perlmutter CPU node, 128 workers (job 60159879); controls and the collection and lift stages on an Apple silicon laptop", "llm": [ { "model": "claude-fable-5-1", "role": "designed the plane census and the lift, wrote the runner and the certificate" } ] } }, { "slug": "qubit_sqrtT-m6-upper-12", "file": "bounds/qubit_sqrtT-m6-upper-12.json", "orbit": "qubit_sqrtT", "m": 6, "direction": "upper", "rank": 12, "tier": "verified", "ok": true, "date": "2026-10-23", "author": "this repository", "reference": "stabrank research/constructions/product_witness.py", "method": "structured construction", "pull_request": 189, "merge_commit": "68e582eb026329fdea029935db0edc444c4792d2", "merge_date": "2026-10-24", "added_commit": "e2ff283573744c9c5195cfc69240298b45278563", "added_date": "2026-10-24", "added_subject": "sqrt(T): chi(R^4) = 5, chi(R^5) = 6, chi(R^6) >= 7 through the Galois-forced subspace (exact census and attested rank-6 census), and chi(R^7) <= 12 from the annealer", "receipt": "certs/qubit_sqrtT-m6-upper-12.json", "receipt_matches": true, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.001, "wall_clock_hours": 0.001, "runs": 1, "hardware": "Apple silicon laptop, one core; direct construction, no search" } }, { "slug": "qubit_sqrtT-m7-lower-7", "file": "bounds/qubit_sqrtT-m7-lower-7.json", "orbit": "qubit_sqrtT", "m": 7, "direction": "lower", "rank": 7, "tier": "attested", "ok": true, "date": "2026-10-23", "author": "Vincent Russo", "reference": "this repository (stabrank-research, round 33)", "method": "projection monotonicity applied to the attested slice-and-lift bound chi(|sqrtT>^6) >= 7", "pull_request": 189, "merge_commit": "68e582eb026329fdea029935db0edc444c4792d2", "merge_date": "2026-10-24", "added_commit": "e2ff283573744c9c5195cfc69240298b45278563", "added_date": "2026-10-24", "added_subject": "sqrt(T): chi(R^4) = 5, chi(R^5) = 6, chi(R^6) >= 7 through the Galois-forced subspace (exact census and attested rank-6 census), and chi(R^7) <= 12 from the annealer", "receipt": "certs/qubit_sqrtT-m7-lower-7.json", "receipt_matches": true, "certificate_script": "verify_challenge/cert_sqrtt_m6_rank6_attested.py", "certificate_budget_s": 3600, "certificate_attested": { "batches": "research/sqrtt_m5_rank6/batch_manifest.json", "recomputed": 2, "compute_hours": 46.3, "hardware": "Perlmutter CPU node (two AMD EPYC 7763, 128 worker processes), NERSC job 60159879, 2026-10-23 16:04 to 16:41 UTC; the representatives stage single-threaded (846 s), the pivot census 46.1 CPU-h over 128 workers (about 23 min wall)", "note": "The complete list of six-term stabilizer decompositions of |sqrtT>^5 lives in the stored batch outputs under research/sqrtt_m5_rank6/results/: for each of the 8,585 orbit representatives of the five-qubit stabilizer states under S_5 x , the residue classes modulo V4 + span(pivot) under two primes and every class that could carry a decomposition (one candidate set in all, the 18 symmetric states). The certificate re-enumerates the dictionary and checks its hash, verifies that the stored pivots meet every orbit exactly once, re-runs two blocks from scratch (seed printed) and compares them byte for byte, re-decides the candidate set exactly over Q(zeta_16) (3,375 decompositions, their exact coefficients), closes the list under the group, and runs the lift to six copies in full; completeness rests on the stored outputs and on research/sqrtt_m5_rank6/census.py, which regenerates any block (census.py run 5 OUT --pivots ...).", "total": 859 }, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 0.0, "wall_clock_hours": 0.0, "runs": 0, "hardware": "none beyond the m = 6 certificate, which prints this line from the same computation" } }, { "slug": "qubit_sqrtT-m7-upper-12", "file": "bounds/qubit_sqrtT-m7-upper-12.json", "orbit": "qubit_sqrtT", "m": 7, "direction": "upper", "rank": 12, "tier": "verified", "ok": true, "date": "2026-10-23", "author": "Vincent Russo", "reference": "stabrank autoresearch/run.py on Perlmutter (round 33 of stabrank-research, job 60161156)", "method": "simulated annealing at rank 12 (8 chains, 8000 iterations per temperature, cooling 0.995), then exact refit", "pull_request": 189, "merge_commit": "68e582eb026329fdea029935db0edc444c4792d2", "merge_date": "2026-10-24", "added_commit": "e2ff283573744c9c5195cfc69240298b45278563", "added_date": "2026-10-24", "added_subject": "sqrt(T): chi(R^4) = 5, chi(R^5) = 6, chi(R^6) >= 7 through the Galois-forced subspace (exact census and attested rank-6 census), and chi(R^7) <= 12 from the annealer", "receipt": "certs/qubit_sqrtT-m7-upper-12.json", "receipt_matches": true, "certificate_script": null, "certificate_budget_s": null, "certificate_attested": null, "lean_module": null, "lean_theorem": null, "lean_receipt": null, "lean_receipt_ok": null, "compute": { "cpu_hours": 22.7452, "wall_clock_hours": 8.5804, "runs": 37, "hardware": "x86_64 Linux, 256 cores", "llm": [ { "model": "claude-fable-5-1", "role": "drove the search" } ] } } ] }