χ_R(∣S⟩^⊗1) ≤ 2

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

lean strange_m1_stabRank_le_two in LeanProofs.M1StabRank, machine-checked by Lean

Implied per-copy exponent γ ≤ 0.6309 against a published 0.3155, no improvement.

Lean proof

This bound is backed by a machine-checked theorem: strange_m1_stabRank_le_two in LeanProofs.M1StabRank. The recorded lake build confirms it compiles.

Notes

single copy Witness: |1⟩ and |2⟩, verified here. The support {1,2} has two points and so is not an affine flat, which is the rank-1 exclusion.

Attribution

Labib and Russo · arXiv:2605.28586 · literature

Submission

JSON

{
  "schema_version": "0.1",
  "orbit": "S",
  "m": 1,
  "direction": "upper",
  "rank": 2,
  "provenance": {
    "author": "Labib and Russo",
    "reference": "arXiv:2605.28586",
    "method": "literature",
    "date": "2026-05-27",
    "github": [
      "FarLab",
      "vprusso"
    ]
  },
  "notes": "single copy Witness: |1> and |2>, verified here. The support {1,2} has two points and so is not an affine flat, which is the rank-1 exclusion.",
  "witness": {
    "terms": [
      {
        "k": 0,
        "x0": [
          1
        ],
        "W": [],
        "Q": [],
        "l": []
      },
      {
        "k": 0,
        "x0": [
          2
        ],
        "W": [],
        "Q": [],
        "l": []
      }
    ],
    "coeffs": [
      "sqrt(2)/2",
      "-sqrt(2)/2"
    ]
  },
  "lean": {
    "module": "LeanProofs.M1StabRank",
    "theorem": "strange_m1_stabRank_le_two"
  }
}