χR(∣H3⟩⊗4) ≥ 3

H₃ 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.

← back to the board

Verification

reproduced   certificate script asserted: CERTIFIED chi(H3^4) >= 3

Compute

1 run; 0.05 CPU-hours; 0.03 h wall-clock; on Apple silicon laptop, one core.

Notes

Closes this cell as a route to the published exponent, which would need rank 2 here. The dictionary is enumerated as int8 phase codes in about 30 s and 600 MB (the complex form is 4.8 GB), and the rank-2 test is one canonicalise-and-sort over quotient directions, so the certificate runs in about two minutes against the 2.2 hours of the streaming version proposed in PR #20, which this supersedes. The exclusion is numerical and rests on a margin: the closest any two key-adjacent quotient directions come to parallel is reported by the script and must clear 1 - 1e-6 by 0.01. A rank-3 exclusion for the same cell has also been run here (χ ≥ 4) and exceeds the default certificate budget.

Attribution

this repository · stabrank rank_exclusion_codes.py · rank-2 exclusion over all 7,439,040 four-qutrit stabilizer states, held as phase codes

Submission

JSON
{
  "schema_version": "0.1",
  "orbit": "H3",
  "m": 4,
  "direction": "lower",
  "rank": 3,
  "certificate": {
    "script": "verify_challenge/cert_h3_m4_rank2.py",
    "expect": "CERTIFIED chi(H3^4) >= 3"
  },
  "provenance": {
    "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",
    "date": "2026-09-18",
    "github": [
      "vprusso"
    ],
    "compute": {
      "cpu_hours": 0.05,
      "wall_clock_hours": 0.03,
      "runs": 1,
      "hardware": "Apple silicon laptop, one core"
    }
  },
  "notes": "Closes this cell as a route to the published exponent, which would need rank 2 here. The dictionary is enumerated as int8 phase codes in about 30 s and 600 MB (the complex form is 4.8 GB), and the rank-2 test is one canonicalise-and-sort over quotient directions, so the certificate runs in about two minutes against the 2.2 hours of the streaming version proposed in PR #20, which this supersedes. The exclusion is numerical and rests on a margin: the closest any two key-adjacent quotient directions come to parallel is reported by the script and must clear 1 - 1e-6 by 0.01. A rank-3 exclusion for the same cell has also been run here (chi >= 4) and exceeds the default certificate budget."
}