χR(∣qubit_H⟩⊗9) ≥ 6

H-type orbit, qubit.

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 · 2/180 re-run   certificate script asserted: CERTIFIED chi(qubit_H^9) >= 6; re-ran 2 of 180 stored batches from scratch chosen from seed 20260921 and only checked the SHA-256 of the other 178 against research/h6_rank5/batch_manifest.json; the full enumeration (73.4 CPU-h on 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) was not re-run

Compute

0 runs; 0 CPU-hours; 0 h wall-clock; on none beyond the m=6 certificate, which this cell re-runs.

Notes

χ(ψ ⊗ φ) ≥ χ(ψ) when φ has a nonzero computational amplitude, applied 3 times to χ(qubit_H^6) ≥ 6. The certificate is the m=6 attested one, which prints this line after certifying the exclusion, so the cell inherits the attested tier. Puts the cell at 6 ≤ χ ≤ 18; the cell had no lower bound before. Completeness rests on the stored batch outputs under research/h6_rank5 and the committed runner that regenerates any of them, exactly as for qubit_H-m6-lower-6.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/h6_rank5 · projection monotonicity applied to the attested exact rank-5 exclusion at m=6

Submission

JSON
{
  "schema_version": "0.1",
  "orbit": "qubit_H",
  "m": 9,
  "direction": "lower",
  "rank": 6,
  "certificate": {
    "script": "verify_challenge/cert_qubit_h_m6_rank5_attested.py",
    "expect": "CERTIFIED chi(qubit_H^9) >= 6",
    "budget_s": 3600,
    "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)."
    }
  },
  "provenance": {
    "author": "this repository",
    "reference": "stabrank research/h6_rank5",
    "method": "projection monotonicity applied to the attested exact rank-5 exclusion at m=6",
    "date": "2026-10-17",
    "github": [
      "vprusso"
    ],
    "compute": {
      "cpu_hours": 0.0,
      "wall_clock_hours": 0.0,
      "runs": 0,
      "hardware": "none beyond the m=6 certificate, which this cell re-runs"
    }
  },
  "notes": "chi(psi (x) phi) >= chi(psi) when phi has a nonzero computational amplitude, applied 3 times to chi(qubit_H^6) >= 6. The certificate is the m=6 attested one, which prints this line after certifying the exclusion, so the cell inherits the attested tier. Puts the cell at 6 <= chi <= 18; the cell had no lower bound before. Completeness rests on the stored batch outputs under research/h6_rank5 and the committed runner that regenerates any of them, exactly as for qubit_H-m6-lower-6.json; the enumeration is not re-run under the budget, and the certificate re-runs the declared batches from scratch and hashes the rest."
}