χR(∣N⟩⊗6) ≥ 7

Norrell orbit, qutrit.

Participate

Run it yourself, or point a coding agent at it.

git clone https://github.com/unitaryfoundation/stabrank
cd stabrank
# describe your decomposition in bounds/mybound.json
make fit BOUND=bounds/mybound.json ARGS=--write
make verify BOUND=bounds/mybound.json

fit solves for the exact coefficients, or tells you no exact combination of your terms reproduces the target. verify rebuilds the identity in exact arithmetic. If it passes, open a pull request adding the file and the leaderboard picks it up on the next build.

A bound the pipeline cannot check is recorded as cited and never takes a record.

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Verification

attested · 2/1057 re-run   certificate script asserted: CERTIFIED chi(N^6) >= 7; re-ran 2 of 1057 stored batches from scratch chosen from seed 20260925 and only checked the SHA-256 of the other 1055 against research/n4_rank6/batch_manifest.json; the full enumeration (121.5 CPU-h on 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/) was not re-run

Compute

0 runs; 0 CPU-hours; 0 h wall-clock; on none beyond the m=4 certificate, which this cell re-runs.

Notes

χ(ψ ⊗ φ) ≥ χ(ψ) when φ has a nonzero computational amplitude, applied 2 times to χ(N^4) ≥ 7. The certificate is the m=4 attested one, which prints this line after certifying the exclusion, so the cell inherits the attested tier. Puts the cell at 7 ≤ χ ≤ 16; the cell had no lower bound before. Completeness rests on the stored batch outputs under research/n4_rank6 and the committed runner that regenerates any of them, exactly as for N-m4-lower-7.json; the enumeration is not re-run under the budget, and the certificate re-runs the declared batches from scratch and hashes the rest.

Attribution

this repository · stabrank research/n4_rank6 · projection monotonicity applied to the attested exact rank-6 exclusion at m=4

Submission

JSON
{
  "schema_version": "0.1",
  "orbit": "N",
  "m": 6,
  "direction": "lower",
  "rank": 7,
  "certificate": {
    "script": "verify_challenge/cert_n_m4_rank6_attested.py",
    "expect": "CERTIFIED chi(N^6) >= 7",
    "budget_s": 3600,
    "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)."
    }
  },
  "provenance": {
    "author": "this repository",
    "reference": "stabrank research/n4_rank6",
    "method": "projection monotonicity applied to the attested exact rank-6 exclusion at m=4",
    "date": "2026-10-17",
    "github": [
      "vprusso"
    ],
    "compute": {
      "cpu_hours": 0.0,
      "wall_clock_hours": 0.0,
      "runs": 0,
      "hardware": "none beyond the m=4 certificate, which this cell re-runs"
    }
  },
  "notes": "chi(psi (x) phi) >= chi(psi) when phi has a nonzero computational amplitude, applied 2 times to chi(N^4) >= 7. The certificate is the m=4 attested one, which prints this line after certifying the exclusion, so the cell inherits the attested tier. Puts the cell at 7 <= chi <= 16; the cell had no lower bound before. Completeness rests on the stored batch outputs under research/n4_rank6 and the committed runner that regenerates any of them, exactly as for N-m4-lower-7.json; the enumeration is not re-run under the budget, and the certificate re-runs the declared batches from scratch and hashes the rest."
}