Hinge4DStarKernel22Status
plain-language theorem explainer
Status record for the type-(2,2) Regge 4D hinge star-kernel campaign: seven boolean gates tracking closed work (star enumeration, flatness, full-star class kernel) versus still-open items (other hinge orbits, flat Hessian assembly, EH 4d convergence, gap-action recovery). Gravity analysts cite the concrete witness that fills these flags. Pure structure definition; no proof content.
Claim. A seven-flag status bundle for the type-$(2,2)$ Regge hinge star: whether star enumeration is closed, whether the flatness gate is closed, whether the full-star deficit class kernel is closed, and whether other hinge orbits, flat Hessian assembly, Einstein–Hilbert $4$d convergence, and gap-action recovery remain open.
background
This module continues the QG full-theory campaign one kernel past the type-$(1,1)$ seed orbit. Scope is the type-$(2,2)$ triangle hinge ${0, e_0+e_1, e_0+e_1+e_2+e_3}$ (masks ${0,3,15}$, difference masks $(3,12)$) and its full periodic Freudenthal star on the $15$-class edge stencil.
Deliverables already proved in-module include: exactly four (cube translate, Kuhn simplex) pairs contain the hinge; all four incident simplices have flat cosine $0$; the star angle sum is exactly $2\pi$; and the full-star deficit class kernel on all $15$ stencil classes has an explicit closed form. The structure below does not restate those theorems; it only packages campaign-level open/closed flags.
Upstream layers (Freudenthal incidence, $15$-class stencil, Gram-projection cosine calculus) are imported and never redefined.
proof idea
No proof: this is a structure declaration with seven Bool fields. Downstream code supplies a single inhabitant that hard-codes the current campaign state. There are no tactics, lemmas, or algebraic reductions at this declaration.
why it matters
Gives a single typed dashboard for the type-$(2,2)$ star-kernel increment so later gravity assembly can read closed versus open gates without re-parsing the module. The sole downstream use is the concrete witness hinge4DStarKernel22Status, which sets star enumeration, flatness, and full-star class kernel to closed, and leaves other hinge orbits, flat Hessian assembly, EH $4$d convergence, and gap-action recovery open (matching the module tier tags).
In the broader Recognition gravity stack this sits under Regge discrete curvature toward continuum Einstein–Hilbert recovery. It does not itself touch T0–T8 forcing, the RCL, or the $\phi$-ladder mass formula; it is a local QG bookkeeping object on the path to those continuum claims.
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