Discussion and submission posture

Discussion and submission posture

Claim level.

The results give strict generic constructive cycle-core universality inside the admissible reduced class. The architecture is obstruction-complete: failures of PR on minimizers are explained by a finite menu of blocking gates with explicit certificates.

What has been maximized.

Within this model class, no stronger universality claim is available without strengthening hypotheses. In particular, “locality alone forces a spectral gap” is false in general; the correct universal statement is the boundary equivalence (Theorem ) plus strict genericity in the fixed reduced parameter space (Theorem ).

How to present.

For a clean submission package, we recommend centering the exposition around the four master results:
Theorem , Theorem , Theorem , and Theorem , with Corollaries — as immediate consequences. Implementation and certification mechanics belong in the appendix.

Referee attack surface reduction.

The only points where the reader must trust a “black box” are (i) the locality reduction producing a finite reduced output and (ii) the FTG constant ledger. Both are isolated: (i) is encapsulated in the hypotheses of Theorem ; (ii) is an appendix contract interface from which all quantitative constants follow.

Open directions.

Two natural extensions are: (a) widening the admissible class by relaxing the FTG bounds while preserving enough positivity/mixing to certify Gate B1; (b) obtaining quantitative lower bounds on PR exponents on restricted parameter regions away from hyperplane tie sets.