verified 75 stabilizer terms reproduce |T5>^{ot 5}, checked symbolically
Implied per-copy exponent γ ≤ 0.5365 against a baseline 0.6826 (single-copy product bound; no published exponent), an improvement.
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, T5-m3-upper-15.json: χ(|T5⟩⊗2) ≤ 5 x χ(|T5⟩⊗3) ≤ 15 gives χ(|T5⟩⊗5) ≤ 75, exponent 0.5365. First witness for this cell. 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.
this repository · stabrank research/constructions/product_witness.py · structured construction
{
"schema_version": "0.1",
"orbit": "T5",
"m": 5,
"direction": "upper",
"rank": 75,
"provenance": {
"author": "this repository",
"reference": "stabrank research/constructions/product_witness.py",
"method": "structured construction",
"date": "2026-10-17",
"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, T5-m3-upper-15.json: chi(|T5>^2) <= 5 x chi(|T5>^3) <= 15 gives chi(|T5>^5) <= 75, exponent 0.5365. First witness for this cell. 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.",
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"-1/20 + sqrt(10)*(10*sqrt(2) - 4*sqrt(5)*I*sqrt(sqrt(5) + 5))/400",
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"1/5",
"(-5 + 5*sqrt(5) + sqrt(10)*I*sqrt(sqrt(5) + 5))*exp(-4*I*pi/5)/100",
"(5 + sqrt(5)*I*sqrt(5 - 2*sqrt(5)))*exp(-4*I*pi/5)/50",
"sqrt(10)*(2*sqrt(10)*(-sqrt(5) - 1)*exp(2*I*pi/5) - 4*sqrt(5)*I*sqrt(5 - sqrt(5))*exp(2*I*pi/5))*exp(-4*I*pi/5)/400"
]
}
}