lean qubit_t_m5_stabRankP_le_six in LeanProofs.QubitTM5StabRank, machine-checked by Lean
Implied per-copy exponent γ ≤ 0.5170 against a published 0.3962, no improvement.
This bound is backed by a machine-checked theorem: qubit_t_m5_stabRankP_le_six in LeanProofs.QubitTM5StabRank. The recorded lake build confirms it compiles.
1 run; 0.001 CPU-hours; 0.001 h wall-clock; on Apple silicon laptop.
First entry for this cell. Witness: the products of the three m=4 terms with |0⟩ and |1⟩; γ = log_2(6)/5 = 0.517, above the published 0.3963, so this fills the cell. Beating the exponent at m=5 would need rank 3, and rank 5 (γ 0.464) would be the first non-product entry; the annealer is being run at rank 5 through autoresearch/run.py. Now at the lean tier: qubit_t_m5_stabRankP_le_six in LeanProofs.QubitTM5StabRank proves stabRankP 2 |qubitT⟩⊗5 ≤ 6 against IsStabP 2 from this witness, the pointwise identity being decided by the kernel on integer coordinate vectors (see lean_proofs/LeanProofs/Stabilizer/Reflect.lean).
this repository · product of board witnesses · tensor product of verified lower-m witnesses
{
"schema_version": "0.1",
"orbit": "qubit_T",
"m": 5,
"direction": "upper",
"rank": 6,
"lean": {
"module": "LeanProofs.QubitTM5StabRank",
"theorem": "qubit_t_m5_stabRankP_le_six"
},
"witness": {
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],
"coeffs": [
"sqrt(5*sqrt(3)/54 + 1/6) + I*sqrt(1/18 - sqrt(3)/54)",
"sqrt(1/18 - sqrt(3)/54) + I*sqrt(1/6 - sqrt(3)/18)",
"sqrt(2*sqrt(3)/27 + 2/9)",
"sqrt(1/9 - sqrt(3)/27) + I*sqrt(1/9 - sqrt(3)/27)",
"sqrt(5*sqrt(3)/54 + 1/6) - I*sqrt(1/18 - sqrt(3)/54)",
"sqrt(1/6 - sqrt(3)/18) + I*sqrt(1/18 - sqrt(3)/54)"
]
},
"provenance": {
"author": "this repository",
"reference": "product of board witnesses",
"method": "tensor product of verified lower-m witnesses",
"date": "2026-09-18",
"github": [
"vprusso"
],
"compute": {
"cpu_hours": 0.001,
"wall_clock_hours": 0.001,
"runs": 1,
"hardware": "Apple silicon laptop"
}
},
"notes": "First entry for this cell. Witness: the products of the three m=4 terms with |0> and |1>; gamma = log_2(6)/5 = 0.517, above the published 0.3963, so this fills the cell. Beating the exponent at m=5 would need rank 3, and rank 5 (gamma 0.464) would be the first non-product entry; the annealer is being run at rank 5 through autoresearch/run.py. Now at the lean tier: qubit_t_m5_stabRankP_le_six in LeanProofs.QubitTM5StabRank proves stabRankP 2 |qubit_T>^5 <= 6 against IsStabP 2 from this witness, the pointwise identity being decided by the kernel on integer coordinate vectors (see lean_proofs/LeanProofs/Stabilizer/Reflect.lean)."
}