χR(∣cat⟩⊗8) ≥ 4

magic cat orbit, m qubits.

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.

← back to the board

Verification

verified   certificate script asserted: CERTIFIED chi(cat_8) >= 4, by an argument declared exact throughout (no floating-point margin)

Compute

0 runs; 0 CPU-hours; 0 h wall-clock; on none beyond the m=7 certificate, which this cell re-runs.

Notes

χ(cat_8) ≥ χ(cat_7) ≥ 4: (I ⊗ ⟨0|)|cat8⟩ = 2^{-1/2}|cat7⟩, checked by the certificate on the exact amplitudes before the claim is printed, and the projection lemma of cert_s_m4_from_m3.py; χ(cat_7) ≥ 4 is bounds/cat-m7-lower-4.json, which the same script re-runs (460 s on one core; budget declared for slower CI runners). Beyond the published values as of our literature check (Oct 2026): QPG (arXiv:2106.07740) list 3 ≤ χ(cat_8) ≤ 6. Jardine's Zenodo deposits (2026-08) report evidence against rank 5 for cat_8; not used here. Puts the cell at 4 ≤ χ ≤ 6; ranks 4 and 5 would still beat log_2(3)/4 through log_2(χ)/(m-2).

Attribution

Michel de Messieres · stabrank verify_challenge · projection monotonicity applied to the slice-and-lift exclusion χ(cat_7) ≥ 4

Submission

JSON
{
  "schema_version": "0.1",
  "orbit": "cat",
  "m": 8,
  "direction": "lower",
  "rank": 4,
  "certificate": {
    "script": "verify_challenge/cert_cat_m7_lift.py",
    "exact": true,
    "budget_s": 1800,
    "expect": "CERTIFIED chi(cat_8) >= 4"
  },
  "provenance": {
    "author": "Michel de Messieres",
    "reference": "stabrank verify_challenge",
    "date": "2026-10-16",
    "github": [
      "MicheldeMessieres"
    ],
    "method": "projection monotonicity applied to the slice-and-lift exclusion chi(cat_7) >= 4",
    "compute": {
      "cpu_hours": 0,
      "wall_clock_hours": 0,
      "runs": 0,
      "hardware": "none beyond the m=7 certificate, which this cell re-runs"
    }
  },
  "notes": "chi(cat_8) >= chi(cat_7) >= 4: (I (x) <0|)|cat_8> = 2^{-1/2}|cat_7>, checked by the certificate on the exact amplitudes before the claim is printed, and the projection lemma of cert_s_m4_from_m3.py; chi(cat_7) >= 4 is bounds/cat-m7-lower-4.json, which the same script re-runs (460 s on one core; budget declared for slower CI runners). Beyond the published values as of our literature check (Oct 2026): QPG (arXiv:2106.07740) list 3 <= chi(cat_8) <= 6. Jardine's Zenodo deposits (2026-08) report evidence against rank 5 for cat_8; not used here. Puts the cell at 4 <= chi <= 6; ranks 4 and 5 would still beat log_2(3)/4 through log_2(chi)/(m-2)."
}