χ_R(∣H3⟩^⊗1) ≥ 2

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

verified certificate script asserted: CERTIFIED chi(H3^1) >= 2, by an argument declared exact throughout (no floating-point margin)

Notes

Settles χ(H3) = 2 with the rank-2 witness of the same cell. Exact throughout: a stabilizer state has one modulus on its support, and the moduli √((3 + √3)/6) and √((3 - √3)/12) differ, decided in sympy. The single-copy cell carries the trivial exponent and moves nothing; it is filed so the orbit page shows χ = 2 at m = 1 as it does for S, T3, and T5.

Attribution

this repository · stabrank verify_challenge · exact: the state is not a stabilizer state (the moduli √((3 + √3)/6) and √((3 - √3)/12) differ)

Submission

JSON

{
  "schema_version": "0.1",
  "orbit": "H3",
  "m": 1,
  "direction": "lower",
  "rank": 2,
  "certificate": {
    "script": "verify_challenge/cert_rank1_moduli.py",
    "expect": "CERTIFIED chi(H3^1) >= 2",
    "exact": true
  },
  "provenance": {
    "author": "this repository",
    "reference": "stabrank verify_challenge",
    "method": "exact: the state is not a stabilizer state (the moduli sqrt((3 + sqrt3)/6) and sqrt((3 - sqrt3)/12) differ)",
    "date": "2026-10-17",
    "github": [
      "vprusso"
    ]
  },
  "notes": "Settles chi(H3) = 2 with the rank-2 witness of the same cell. Exact throughout: a stabilizer state has one modulus on its support, and the moduli sqrt((3 + sqrt3)/6) and sqrt((3 - sqrt3)/12) differ, decided in sympy. The single-copy cell carries the trivial exponent and moves nothing; it is filed so the orbit page shows chi = 2 at m = 1 as it does for S, T3, and T5."
}