hinge4DFlatKernelStatus
plain-language theorem explainer
Status snapshot for the 4D Regge hinge flat-kernel campaign: the Freudenthal 24-simplex enumeration and seed-hinge incidence layer are marked closed, while true per-hinge deficit kernels stay open and both EH 4d convergence and gap-action recovery are explicitly false. Gravity analysts cite it as the honest gate record for deliverable B. It is a five-field structure literal, not a derived proof.
Claim. The hinge flat-kernel status record sets: Freudenthal 24-simplex enumeration closed ($\mathrm{true}$); seed-hinge incidence closed ($\mathrm{true}$); true deficit kernels still open ($\mathrm{true}$); convergence of the RS action to 4d Einstein–Hilbert ($\mathrm{false}$); gap-action recovery ($\mathrm{false}$).
background
This module is the next kernel-checked increment after the 15-class 4D Regge edge stencil. It treats the Freudenthal/Kuhn triangulation of the 4-cube: 24 monotone 4-simplices (axis permutations), each with five nested vertices and ten edge-class masks drawn from the imported stencil. The seed hinge is the triangle on vertices $0$, $e_0$, $e_0+e_1$ (masks $0,1,3$); exactly two of the 24 simplices contain it.
The status structure packages five boolean gates. Combinatorial deliverables (enumeration, incidence multiplicities, nonvacuity, axis-swap symmetry, decoy classes) are intended closed. The true per-hinge flat second-variation kernels (dihedral/Cayley–Menger class weights) remain OPEN parameters in the MODEL assembly formula. The module doc states explicitly that this does not complete the flat Hessian, does not prove RS-to-EH 4d convergence, and does not flip gap-action recovery.
proof idea
Pure definition: a structure literal for the five-field status record. Each field is assigned a concrete Bool (true for the two combinatorial closures and the open-kernel flag; false for EH 4d convergence and gap-action recovery). No lemmas, tactics, or computation.
why it matters
Pins the campaign's honest scope inside the QG full-theory stack: combinatorial support closed, analytic kernels and continuum limits not claimed. Downstream, hinge4DFlatKernelStatus_flags reifies the five equalities as a single conjunction theorem, so later modules can pattern-match on the gate vector rather than restate policy. Aligns with the module tier tags (THEOREM vs MODEL vs OPEN) and blocks reverse-engineering weights from Einstein–Hilbert. Does not touch T0–T8 forcing, RCL, or the phi-ladder mass formula; it is pure discrete-gravity scaffolding toward a future flat Hessian of the 4D Regge action.
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