χR(∣qubit_sqrtT⟩⊗3) ≥ 4

√T orbit, qubit.

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(qubit_sqrtT^3) >= 4, by an argument declared exact throughout (no floating-point margin)

Compute

1 run; 0.003 CPU-hours; 0.003 h wall-clock; on Apple silicon laptop, one core; about 10 s for the certificate; claude-fable-5-1, found the descent argument and wrote the certificate.

Notes

Settles χ(|sqrtT⟩⊗3) = 4 with the four-term witness. Galois descent: the four conjugates (1, zeta^k)^3 of the target, k = 1, 5, 9, 13, restricted to one string of each Hamming weight 0 to 3 form a Vandermonde matrix in zeta, zeta^5, -zeta, -zeta^5, so they are independent and any stabilizer span containing the target has dimension at least 4; from m = 3 on the argument gives 4 for every m. Exact: computed as a rank over Q(zeta_16). Replaces the numerical pivot-search exclusion of the research survey (1,080 states, 185 pivots, closest approach 0.9981, too thin for the 0.01 margin of rank_exclusion.py).

Attribution

Vincent Russo · stabrank verify_challenge · Galois descent over Z[i]: the four conjugates of the target under Gal(Q(zeta_16)/Q(i)) span a space of dimension min(4, m + 1); no search

Submission

JSON
{
  "schema_version": "0.1",
  "orbit": "qubit_sqrtT",
  "m": 3,
  "direction": "lower",
  "rank": 4,
  "certificate": {
    "script": "verify_challenge/cert_sqrtt_galois.py",
    "expect": "CERTIFIED chi(qubit_sqrtT^3) >= 4",
    "exact": true
  },
  "provenance": {
    "author": "Vincent Russo",
    "reference": "stabrank verify_challenge",
    "method": "Galois descent over Z[i]: the four conjugates of the target under Gal(Q(zeta_16)/Q(i)) span a space of dimension min(4, m + 1); no search",
    "date": "2026-10-21",
    "github": [
      "vprusso"
    ],
    "compute": {
      "cpu_hours": 0.003,
      "wall_clock_hours": 0.003,
      "runs": 1,
      "hardware": "Apple silicon laptop, one core; about 10 s for the certificate",
      "llm": [
        {
          "model": "claude-fable-5-1",
          "role": "found the descent argument and wrote the certificate"
        }
      ]
    }
  },
  "notes": "Settles chi(|sqrtT>^3) = 4 with the four-term witness. Galois descent: the four conjugates (1, zeta^k)^3 of the target, k = 1, 5, 9, 13, restricted to one string of each Hamming weight 0 to 3 form a Vandermonde matrix in zeta, zeta^5, -zeta, -zeta^5, so they are independent and any stabilizer span containing the target has dimension at least 4; from m = 3 on the argument gives 4 for every m. Exact: computed as a rank over Q(zeta_16). Replaces the numerical pivot-search exclusion of the research survey (1,080 states, 185 pivots, closest approach 0.9981, too thin for the 0.01 margin of rank_exclusion.py)."
}