lean t5_m4_stabRankP_le_twentyfive in LeanProofs.T5M4StabRank, machine-checked by Lean
Implied per-copy exponent γ ≤ 0.5000 against a baseline 0.6826 (single-copy product bound; no published exponent), an improvement.
This bound is backed by a machine-checked theorem: t5_m4_stabRankP_le_twentyfive in LeanProofs.T5M4StabRank. The recorded lake build confirms it compiles.
1 run; 0.001 CPU-hours; 0.001 h wall-clock; on Apple silicon laptop, one core; direct construction, no search.
Tensor product of the exact decompositions T5-m2-upper-5.json (taken 2 times): χ(|T5⟩⊗2) ≤ 5 x χ(|T5⟩⊗2) ≤ 5 gives χ(|T5⟩⊗4) ≤ 25, exponent 0.5000. Replaces the rank-64 tensor square of the annealed rank-8 m=2 witness (T5-m4-upper-64.json, 2026-09-23). The orbit has no published exponent and is measured against the single-copy product bound log_5(3) = 0.6826; this exponent is below that baseline because the m=2 factor already is, so it beats no published exponent and the site does not count it as one. It is the sub-multiplicative value the board already implied. Terms are the exact products (x0 and l concatenated, W and Q block diagonal) and coefficients the exact products, built by research/constructions/product_witness.py. Lean: t5_m4_stabRankP_le_twentyfive in LeanProofs.T5M4StabRank proves stabRankP 5 |T5⟩⊗4 ≤ 25 from the m=2 theorem and the multiplicativity lemma stabRankP_tensor_le; the 25 terms here are the products that lemma counts.
this repository · stabrank research/constructions/product_witness.py · structured construction
{
"schema_version": "0.1",
"orbit": "T5",
"m": 4,
"direction": "upper",
"rank": 25,
"provenance": {
"author": "this repository",
"reference": "stabrank research/constructions/product_witness.py",
"method": "structured construction",
"date": "2026-09-24",
"github": [
"vprusso"
],
"compute": {
"cpu_hours": 0.001,
"wall_clock_hours": 0.001,
"runs": 1,
"hardware": "Apple silicon laptop, one core; direct construction, no search"
}
},
"notes": "Tensor product of the exact decompositions T5-m2-upper-5.json (taken 2 times): chi(|T5>^2) <= 5 x chi(|T5>^2) <= 5 gives chi(|T5>^4) <= 25, exponent 0.5000. Replaces the rank-64 tensor square of the annealed rank-8 m=2 witness (T5-m4-upper-64.json, 2026-09-23). The orbit has no published exponent and is measured against the single-copy product bound log_5(3) = 0.6826; this exponent is below that baseline because the m=2 factor already is, so it beats no published exponent and the site does not count it as one. It is the sub-multiplicative value the board already implied. Terms are the exact products (x0 and l concatenated, W and Q block diagonal) and coefficients the exact products, built by research/constructions/product_witness.py. Lean: t5_m4_stabRankP_le_twentyfive in LeanProofs.T5M4StabRank proves stabRankP 5 |T5>^4 <= 25 from the m=2 theorem and the multiplicativity lemma stabRankP_tensor_le; the 25 terms here are the products that lemma counts.",
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],
"coeffs": [
"1/5",
"exp(2*I*pi/5)/5",
"exp(-4*I*pi/5)/5",
"exp(4*I*pi/5)/5",
"exp(-2*I*pi/5)/5",
"exp(2*I*pi/5)/5",
"exp(4*I*pi/5)/5",
"exp(-2*I*pi/5)/5",
"exp(-4*I*pi/5)/5",
"1/5",
"exp(-4*I*pi/5)/5",
"exp(-2*I*pi/5)/5",
"exp(2*I*pi/5)/5",
"1/5",
"exp(4*I*pi/5)/5",
"exp(4*I*pi/5)/5",
"exp(-4*I*pi/5)/5",
"1/5",
"exp(-2*I*pi/5)/5",
"exp(2*I*pi/5)/5",
"exp(-2*I*pi/5)/5",
"1/5",
"exp(4*I*pi/5)/5",
"exp(2*I*pi/5)/5",
"exp(-4*I*pi/5)/5"
]
},
"lean": {
"module": "LeanProofs.T5M4StabRank",
"theorem": "t5_m4_stabRankP_le_twentyfive"
}
}