χ_R(∣H3⟩^⊗3) ≤ 4

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.

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Verification

lean h3_m3_stabRank_le_four in LeanProofs.M3StabRank, machine-checked by Lean

Implied per-copy exponent γ ≤ 0.4206 against a published 0.4206, no improvement.

Lean proof

This bound is backed by a machine-checked theorem: h3_m3_stabRank_le_four in LeanProofs.M3StabRank. The recorded lake build confirms it compiles.

Notes

tight Now stated against stabRank: h3_m3_stabRank_le_four proves Stabilizer.stabRank IsStab |M⟩^⊗3 ≤ 4 with the four terms shown to be stabilizer states in the concrete sense (two full-support states with phases 2y0^2 + 2y1^2 + y2^2 and y0^2 + y1^2 + 2y2^2, the line |0,0,+> and the plane |+,+,0>). With the exhaustive rank-3 exclusion certificate the cell is settled at 4.

Attribution

Labib and Russo · arXiv:2605.28586 · literature

Submission

JSON

{
  "schema_version": "0.1",
  "orbit": "H3",
  "m": 3,
  "direction": "upper",
  "rank": 4,
  "provenance": {
    "author": "Labib and Russo",
    "reference": "arXiv:2605.28586",
    "method": "literature",
    "date": "2026-05-27",
    "github": [
      "FarLab",
      "vprusso"
    ]
  },
  "notes": "tight Now stated against stabRank: h3_m3_stabRank_le_four proves Stabilizer.stabRank IsStab |M>^3 <= 4 with the four terms shown to be stabilizer states in the concrete sense (two full-support states with phases 2y0^2 + 2y1^2 + y2^2 and y0^2 + y1^2 + 2y2^2, the line |0,0,+> and the plane |+,+,0>). With the exhaustive rank-3 exclusion certificate the cell is settled at 4.",
  "lean": {
    "module": "LeanProofs.M3StabRank",
    "theorem": "h3_m3_stabRank_le_four"
  }
}