IndisputableMonolith.Gravity.Analysis.ReggeHinge4DStarKernelAudit
Audit layer for the Regge 4D periodic-lattice star-deficit kernel: it packages the checks that the full star class, built on the Freudenthal incidence layer and the 15-class stencil, is consistent with the seed two-simplex dihedral cosine calculus. Gravity and discrete-QG workers cite it when they need a kernel-checked increment past the dihedral hinge kernel. Structure is import-and-audit rather than a new constructive proof.
claimAudit module for the 4D Regge star-deficit kernel on a periodic lattice: consistency of the full star class of hinge deficits with the Freudenthal incidence structure, the 15-class stencil, and the two-simplex dihedral cosine calculus, without redefining those APIs.
background
Regge calculus replaces smooth curvature by deficit angles on hinges of a triangulated spacetime. In 4D the natural local object is the star of a hinge: the collection of 4-simplices meeting on a shared triangle (or edge, depending on the dual picture), whose dihedral angles determine the deficit.
The upstream kernel module states the QG full-theory campaign increment after the dihedral hinge kernel: it imports the Freudenthal incidence layer, the 15-class stencil, and the seed two-simplex dihedral cosine calculus, and never redefines their API. This audit module sits on that import and records the formal checks that the star-deficit class is well-typed and kernel-consistent under those fixed interfaces.
Setting is discrete gravity analysis inside the Recognition Science gravity stack: lattice-periodic 4D Regge data, class-indexed deficits, and cosine-level dihedral geometry as the computational seed.
proof idea
This is an audit module, not a constructive theorem file. It imports the star-deficit kernel and organizes verification that the full periodic-lattice star class respects the already-fixed Freudenthal incidence, 15-class stencil, and two-simplex dihedral cosine APIs. Expect type-level and equality-level consistency lemmas, or thin wrappers that re-export kernel facts under audit names, rather than a long independent derivation.
why it matters in Recognition Science
In the QG full-theory campaign the star kernel is the next kernel-checked increment after the 4D dihedral hinge kernel. An explicit audit module makes that increment reviewable: referees can see that the star-deficit class does not silently extend or mutate the incidence and cosine layers it depends on.
No downstream consumers are listed yet in the graph, so the module presently closes a local verification gap rather than feeding a named parent theorem. It still matters for the gravity domain stack: without a checked star class, later continuum or continuum-limit claims about 4D Regge curvature cannot honestly cite the lattice kernel. Framework landmarks (forcing chain T0–T8, RCL, phi ladder) are not directly invoked here; the link is through discrete gravity infrastructure that those continuum claims will eventually rest on.
scope and limits
- Does not prove continuum Einstein equations from the lattice star deficits.
- Does not redefine Freudenthal incidence, the 15-class stencil, or dihedral cosine APIs.
- Does not establish dynamical evolution or a path-integral measure on the lattice.
- Does not claim numerical values for physical constants or mass rungs.
- Does not list downstream theorem consumers in the current dependency graph.