IndisputableMonolith.Gravity.Analysis.ReggeHinge4DFlatKernelAudit
Audit layer for the 4D Regge Freudenthal-hinge flat-Hessian kernel. It checks incidence bookkeeping and Hessian assembly against the imported 15-class edge stencil, without redefining geometry. Quantum-gravity and discrete-gravity workers cite it when verifying that the flat-space kernel is kernel-checked before curved or dynamical extensions. Structure is import-and-audit: theorems and identities are re-exported or restated against the upstream skeleton.
claimModule auditing the 4D Regge calculus flat kernel on Freudenthal hinges: incidence relations for hinge–edge–simplex attachment and assembly of the flat-space Hessian of the Regge action, relative to the fixed 15-class edge stencil, with no redefinition of the stencil or of the hinge geometry.
background
Recognition Science gravity work treats discrete spacetime via Regge calculus: curvature lives on hinges (codimension-2 simplices), and the action is linear in deficit angles. In 4D the natural hinge is a triangle; the Freudenthal triangulation supplies a regular lattice scaffolding on which edge lengths and hinge incidences can be enumerated exhaustively.
The upstream module ReggeHinge4DFlatKernel is the next kernel-checked increment after the 4D edge stencil. Its doc states it is the "Regge 4D Freudenthal hinge incidence + flat-Hessian assembly skeleton" in the QG full-theory campaign, and that the 15-class stencil is imported, never redefined. Flat-Hessian means the second variation of the Regge action about a flat background, assembled from hinge incidences and edge-length coordinates.
This audit module sits one layer above that skeleton. It does not introduce new geometric primitives; it re-checks and organizes the incidence and assembly claims so downstream gravity analysis can treat the flat kernel as a stable interface.
proof idea
This is an audit module, not a single theorem. Argument structure is: import the hinge-incidence and flat-Hessian skeleton; keep the 15-class edge stencil fixed; restate or re-export kernel-checked identities (tier-tagged THEOREM in the upstream sense: no sorry) that confirm incidence counts and Hessian assembly match the stencil. No independent geometric construction; verification and packaging of the upstream kernel.
why it matters in Recognition Science
In the RS gravity stack, continuum limits and effective Newtonian or post-Newtonian behaviour need a discrete kernel that is fully checked in flat space before curvature, matter, or recognition-cost couplings are added. The parent campaign is the QG full-theory path begun at the 4D edge stencil and continued in the Freudenthal hinge flat-Hessian skeleton. This audit module has no downstream used_by edges in the graph yet; its role is to freeze the flat kernel interface so later hinge-curvature, deficit-angle, and continuum-matching results can cite a single audited surface rather than raw assembly lemmas. It does not itself touch T8 ($D=3$) or the J-cost forcing chain; those enter only when the discrete kernel is matched to RS continuum gravity.
scope and limits
- Does not redefine the 15-class edge stencil or Freudenthal hinge geometry.
- Does not prove curved-background or dynamical-metric Hessian formulae.
- Does not derive continuum Einstein or Newtonian limits from the kernel.
- Does not couple hinges to recognition-cost, mass ladders, or gauge sectors.
- Does not claim new incidence theorems beyond auditing the upstream skeleton.