attested · 2/160 re-run certificate script asserted: CERTIFIED chi(qubit_T^6) >= 6; re-ran 2 of 160 stored batches from scratch chosen from seed 20260924 and only checked the SHA-256 of the other 158 against research/t5_rank5/batch_manifest.json; the full enumeration (36.4 CPU-h on 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) was not re-run
0 runs; 0 CPU-hours; 0 h wall-clock; on none beyond the m=5 certificate, which this cell re-runs.
χ(ψ ⊗ φ) ≥ χ(ψ) when φ has a nonzero computational amplitude, applied 1 time to χ(T^5) ≥ 6 (Lean: stabRankP_powVecP_mono in lean_proofs/LeanProofs/Stabilizer/SliceP.lean). The certificate is the m=5 attested one, which prints this line after certifying the rank-5 exclusion; the cell inherits the attested tier. With bounds/qubit_T-m6-upper-6.json (Lean tier) this settles χ(T^6) = 6, replacing the lower bound of 5 from the projected rank-4 exclusion.
this repository · stabrank research/t5_rank5 · projection monotonicity applied to the attested exact rank-5 exclusion at m=5
{
"schema_version": "0.1",
"orbit": "qubit_T",
"m": 6,
"direction": "lower",
"rank": 6,
"certificate": {
"script": "verify_challenge/cert_qubit_t_m5_rank5_attested.py",
"expect": "CERTIFIED chi(qubit_T^6) >= 6",
"budget_s": 3600,
"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)."
}
},
"provenance": {
"author": "this repository",
"reference": "stabrank research/t5_rank5",
"method": "projection monotonicity applied to the attested exact rank-5 exclusion at m=5",
"date": "2026-09-24",
"github": [
"vprusso"
],
"compute": {
"cpu_hours": 0.0,
"wall_clock_hours": 0.0,
"runs": 0,
"hardware": "none beyond the m=5 certificate, which this cell re-runs"
}
},
"notes": "chi(psi (x) phi) >= chi(psi) when phi has a nonzero computational amplitude, applied 1 time to chi(T^5) >= 6 (Lean: stabRankP_powVecP_mono in lean_proofs/LeanProofs/Stabilizer/SliceP.lean). The certificate is the m=5 attested one, which prints this line after certifying the rank-5 exclusion; the cell inherits the attested tier. With bounds/qubit_T-m6-upper-6.json (Lean tier) this settles chi(T^6) = 6, replacing the lower bound of 5 from the projected rank-4 exclusion."
}