IndisputableMonolith.Gravity.Analysis.ReggeHinge4DStarKernel13Audit
Audit layer for the Regge 4D type-(1,3) periodic-lattice star deficit kernel. Discrete-QG and gravity workers cite it when confirming that the (1,3) orbit-class kernel stays aligned with the Freudenthal incidence layer, the 15-class stencil, and the Gram-projection cosine calculus. The module is import-and-audit of Kernel13, not a fresh constructive geometry proof.
claimAudit module for the Regge-calculus 4D star deficit kernel on the type-$(1,3)$ periodic-lattice orbit class: consistency checks of hinge deficits against Freudenthal incidence and Gram-projection cosine identities, without redefining those APIs.
background
In the Recognition Science gravity stack, discrete curvature is carried by Regge hinge deficits on a 4D periodic lattice. Star-hinge orbits are typed by pairs; type $(1,3)$ is the next kernel-checked increment after the type-$(1,1)$ seed orbit and the orbit-classification layer.
The upstream module packages that type-$(1,3)$ deficit-class kernel. Per its doc-comment, it is a "QG full-theory campaign" step that "imports the Freudenthal incidence layer, the 15-class stencil, and the Gram-projection cosine calculus; never redefines their API." This audit module sits on that import and records the verification surface for the same campaign.
proof idea
Definition-and-audit module, not a theorem tree. It imports the type-$(1,3)$ star-kernel development and exposes the checked claims. There is no independent tactic or term argument beyond the Kernel13 import edge; structure is "import and audit," not new geometric identities.
why it matters in Recognition Science
Marks the audit waypoint for the type-$(1,3)$ increment in the Regge 4D star-deficit campaign, after the type-$(1,1)$ seed kernel and the orbit-classification layer. Downstream gravity-analysis consumers can treat the $(1,3)$ kernel as kernel-checked once this audit is green. No used_by edges are recorded yet; the module is a verification station on the QG full-theory path rather than a lemma feeder into mass-ladder or continuum limits.
scope and limits
- Does not redefine Freudenthal incidence, 15-class stencil, or Gram-projection APIs.
- Does not treat type-(1,1) or orbit classes other than (1,3).
- Does not claim continuum GR recovery or continuum-limit theorems.
- Does not introduce mass-ladder, RCL, or forcing-chain (T0–T8) identities.
- Does not supply new hinge-deficit constructions beyond auditing Kernel13.