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_gt_one in LeanProofs.StrangeM1Lower, machine-checked by Lean

Lean proof

This bound is backed by a machine-checked theorem: strange_m1_stabRank_gt_one in LeanProofs.StrangeM1Lower. The recorded lake build confirms it compiles.

Notes

Settles χ(S) = 2 with the Lean upper bound strange_m1_stabRank_le_two. Exact throughout: a stabilizer state is supported on an affine flat, of size 1 or 3 for one qutrit, and |S⟩ has support 2. Also proved in Lean against stabRank: StrangeM1Lower.strange_m1_stabRank_gt_one (the support {1, 2} is not closed under a - b + d).

Attribution

this repository · stabrank verify_challenge · exact: the state is not a stabilizer state (support size 2 is not an affine flat of F₃)

Submission

JSON

{
  "schema_version": "0.1",
  "orbit": "S",
  "m": 1,
  "direction": "lower",
  "rank": 2,
  "certificate": {
    "script": "verify_challenge/cert_rank1_moduli.py",
    "expect": "CERTIFIED chi(S^1) >= 2",
    "exact": true
  },
  "provenance": {
    "author": "this repository",
    "reference": "stabrank verify_challenge",
    "method": "exact: the state is not a stabilizer state (support size 2 is not an affine flat of F_3)",
    "date": "2026-09-20",
    "github": [
      "vprusso"
    ]
  },
  "notes": "Settles chi(S) = 2 with the Lean upper bound strange_m1_stabRank_le_two. Exact throughout: a stabilizer state is supported on an affine flat, of size 1 or 3 for one qutrit, and |S> has support 2. Also proved in Lean against stabRank: StrangeM1Lower.strange_m1_stabRank_gt_one (the support {1, 2} is not closed under a - b + d).",
  "lean": {
    "module": "LeanProofs.StrangeM1Lower",
    "theorem": "strange_m1_stabRank_gt_one"
  }
}