χ_R(∣S⟩^⊗4) ≥ 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^4) >= 4

Notes

Projection monotonicity from m=3, with the m=3 exclusion re-run inside the certificate rather than taken from the board: χ(ψ ⊗ φ) ≥ χ(ψ) whenever φ has a nonzero computational amplitude, since applying I ⊗ ⟨x| to a decomposition of ψ ⊗ φ maps each stabilizer state to a stabilizer state or zero (the lemma is written out in the certificate). With the rank-4 upper bound this settles χ(|S⟩^⊗4) = 4.

Attribution

Labib and Russo · arXiv:2605.28586 · literature

Submission

JSON

{
  "schema_version": "0.1",
  "orbit": "S",
  "m": 4,
  "direction": "lower",
  "rank": 4,
  "provenance": {
    "author": "Labib and Russo",
    "reference": "arXiv:2605.28586",
    "method": "literature",
    "date": "2026-05-27",
    "github": [
      "FarLab",
      "vprusso"
    ]
  },
  "notes": "Projection monotonicity from m=3, with the m=3 exclusion re-run inside the certificate rather than taken from the board: chi(psi (x) phi) >= chi(psi) whenever phi has a nonzero computational amplitude, since applying I (x) <x| to a decomposition of psi (x) phi maps each stabilizer state to a stabilizer state or zero (the lemma is written out in the certificate). With the rank-4 upper bound this settles chi(|S>^4) = 4.",
  "certificate": {
    "script": "verify_challenge/cert_s_m4_from_m3.py",
    "expect": "CERTIFIED chi(S^4) >= 4"
  }
}