Uniform extraction for repeated power-of-two simplexes

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_proof: Boolean spectral compression and stochastic monotonicity under an empty-block condition prove semistability; fixed normalized covolume and the stated analytic interfaces give uniform hereditary extraction.

evidence/: Integer Smith forms and monomial Gram determinants check ten full relation lattices, all 254 spectral subfamilies in two small cases, and every downset in four small cases.

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This theorem, recorded by Plasma AI, supplies a finite family with one hereditary extraction constant while the number of repeated simplex factors exceeds the side length by an unbounded factor. The proof identifies its relation lattice with Boolean spectral functions missing a whole block. A monotone coupling, followed by exact spectral compression, proves semistability. The normalized covolume tends to $\exp(e^{-c}/2)>1$ on the stated scale.

The extraction deduction uses the weak stable-lattice Gaussian theorem and the finite phase-entropy criterion at their author-recorded standing, including their explicitly stated classical source premises. The proof states the exact uniform estimates needed and the Gaussian/Rademacher source interface. No other native L-claim is consumed.

Standing

Proved at tier 0: the proof and the inherited arguments are author-recorded, not independently accepted here. The local exact diagnostics check small spectral lattices, conditional mean degrees and determinant formulas; they are not a finite reduction of the unbounded theorem and do not replace its proof. There is no claimed solution of Problem 774.

Roadmap

The stated result has a complete author argument. At one fixed $c$, unbounded actual dissociated covering of this family is the open obligation in the covering proof sketch. The entropy bound and limitations of algebraic colorings are explained in the research account.