recognitionMeshExactJBridge4DStatus_flags
plain-language theorem explainer
Status ledger for the 4D Recognition-mesh exact-J bridge: mesh carrier defined; amplitude Hessian, iterated EH, and true-Regge equality faces closed; gap-action recovery left false; Schläfli elevation left open. Gravity auditors cite it when checking continuum-closure honesty against the Option-C midpoint Bloch program. Proof is pure decidable evaluation of the concrete status record.
Claim. The Recognition-mesh exact-$J$ bridge status record satisfies: mesh carrier defined $=\mathrm{true}$, amplitude Hessian open $=\mathrm{false}$, iterated Einstein-Hilbert open $=\mathrm{false}$, equals-true-Regge open $=\mathrm{false}$, gap-action recovery $=\mathrm{false}$, and Schläfli elevation open $=\mathrm{true}$.
background
This module is the Recognition gate of the 4D continuum-closure campaign. It builds a canonical Recognition mesh carrier on the periodic Freudenthal 4-torus and attaches a value-level action whose amplitude Hessian is the geometric Option-C midpoint Bloch symbol on that torus family.
Preferred limit shape is amplitude Hessian at fixed mesh, then $N\to\infty$. By construction the amplitude Hessian equals the mesh true-Regge Hessian. The iterated continuum face is the scale-explicit Option-C object obtained by composing the discrete torus bridge with the exact midpoint $m^2$ TT and gauge faces. The module does not consume amplitude-scaling refinement families as continuum premises, and it excludes arbitrary test-variation pullback hypotheses.
The status structure is a boolean ledger of which faces are closed versus deliberately left open. Upstream scaffolding (simplicial face maps, forcing-chain bookkeeping) is only incidental to the flag record itself.
proof idea
One-line decidable proof. The status definition hard-codes the six booleans; decide evaluates the conjunction of equalities against those literals and closes.
why it matters
Binding-honesty checkpoint for the QG full-theory campaign. Module doc states as theorems that the amplitude Hessian exists and equals the mesh true-Regge Hessian, and that iterated $N\to\infty$ Tendsto closes at the scale-explicit Option-C EH face, while explicitly refusing to flip gap-action recovery or inhabit the full $S_{\mathrm{RS}}$ converges-to-EH-4d statement. Elevating the Hessian to the literal nonlinear Regge action via Schläfli remains open. This flag theorem freezes that ledger so downstream continuum claims cannot silently overclaim closed faces. No downstream users are wired yet; the declaration is the audit surface itself.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.