PhiLatticeRegularity
plain-language theorem explainer
PhiLatticeRegularity encodes the uniform edge-length property of the φ-lattice for Regge calculus on piecewise-linear manifolds. Researchers working on strong-field gravity would cite it to obtain the Cheeger-Muller-Schrader regularity conditions automatically from the φ-scaling. The structure is assembled directly from four fields that fix the backbone length φ² × 1.47 together with positivity and uniformity.
Claim. A φ-lattice regularity consists of a real number L satisfying 0 < L, uniformity of all edge lengths, and the explicit relation L = φ² · 1.47.
background
The module addresses nonlinear Regge convergence (Q12) in Recognition Science. The linearized regime is already certified; the nonlinear regime requires Cheeger-Muller-Schrader regularity on piecewise-linear manifolds. The φ-lattice supplies this regularity because every edge length is a multiple of the backbone d = φ² × 1.47. The structure therefore encodes exactly the conditions needed for the CMS theorem to apply to the lattice.
proof idea
The declaration is a structure definition. It directly assembles the four fields: edge_length as a real, the positivity predicate, the trivial uniformity predicate, and the equality edge_length = φ² · 1.47.
why it matters
The definition supplies the regularity instance used by canonical_phi_lattice, CMSConditions, and NonlinearReggeCert. It thereby closes the conditional coverage for neutron-star surfaces and horizons while leaving the black-hole interior open. It instantiates the φ-ladder scaling that appears throughout the Recognition Science forcing chain and the eight-tick octave.
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