χ_R(∣S⟩^⊗3) ≥ 4

Strange 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

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

Compute

1 run; 0.05 CPU-hours; 0.05 h wall-clock; on Apple silicon laptop, 8 worker processes.

Notes

The exhaustive m=3 value of arXiv:2605.28586, reproduced here from scratch: every rank-3 triple over the 30240 three-qutrit stabilizer states is excluded by the pivot-and-quotient search of rank_exclusion.py, with rank 2 excluded in the same pass. Together with the Lean-checked rank-4 decomposition this settles χ(|S⟩^⊗3) = 4 with both directions machine-checked. The exclusion is numerical and rests on a margin: the certificate reports the closest any two non-parallel quotient directions come to the parallel threshold and refuses to print its claim if that margin is under 0.01. The Norrell state at m=2, whose rank-3 decomposition is proved in Lean, is the positive control.

Attribution

Labib and Russo · arXiv:2605.28586 · literature

Submission

JSON

{
  "schema_version": "0.1",
  "orbit": "S",
  "m": 3,
  "direction": "lower",
  "rank": 4,
  "provenance": {
    "author": "Labib and Russo",
    "reference": "arXiv:2605.28586",
    "method": "literature",
    "date": "2026-05-27",
    "github": [
      "FarLab",
      "vprusso"
    ],
    "compute": {
      "cpu_hours": 0.05,
      "wall_clock_hours": 0.05,
      "runs": 1,
      "hardware": "Apple silicon laptop, 8 worker processes"
    }
  },
  "notes": "The exhaustive m=3 value of arXiv:2605.28586, reproduced here from scratch: every rank-3 triple over the 30240 three-qutrit stabilizer states is excluded by the pivot-and-quotient search of rank_exclusion.py, with rank 2 excluded in the same pass. Together with the Lean-checked rank-4 decomposition this settles chi(|S>^3) = 4 with both directions machine-checked. The exclusion is numerical and rests on a margin: the certificate reports the closest any two non-parallel quotient directions come to the parallel threshold and refuses to print its claim if that margin is under 0.01. The Norrell state at m=2, whose rank-3 decomposition is proved in Lean, is the positive control.",
  "certificate": {
    "script": "verify_challenge/cert_s_m3_rank3.py",
    "expect": "CERTIFIED chi(S^3) >= 4"
  }
}