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Prove uniform Gaussian boundary conditioning at the production scale - #5479
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The retained full-cell Gaussian boundary theorem holds only for fixed alpha, so it does not justify the source's production choice
alpha=ceil(sqrt((4/pi)log(16p))). This package proves a uniform relative two-edge operator limit fortheta^(1/10) <= b=pi/alpha² <= 1, which contains the actual production scale and its complete theta interval eventually. Normalized q-product ratios remove the previous absolute constants. A corollary gives||K^-1||₂ <= p^(2+eta)eventually for every fixed positive eta, preserving the source's ceiling, floor, phase and complete infinite-product coefficient.The exact untruncated full cell is the scope. This does not admit a capped RawGaussian program, rounded reference, inverse algorithm, physical execution or new kappa. Preparation, truncation, precision, storage, movement and outer recovery remain explicit obligations.
Validation: normal and optimized registered checks; 98 exact elimination comparisons, 7,906 original-source geometry pairs, 216 rescaled exponent comparisons, nonvacuous rational product enclosures and falsifying controls; committed-byte/source-history preflight; official export integrity; isolated Git-free normal/optimized replay; source and receipt mutation rejection. The uniform statement is the written proof, not extrapolation from these finite checks.
Canonical claim: #4202 (comment)
Credit the retained Jose Manuel/#4193, Vlado Vojdanovski/#1673, Cinna Davis/PR4100, Ryanson Jonathan/#4435, Nick Petalas/#5150 and JoyboyBrian boundary-limit lineage, together with the classical q-LDU and product identities. Prepared by JoyboyBrian with substantial OpenAI Codex assistance; Apache-2.0. No independent human or formal-kernel acceptance is claimed.