Mat4
plain-language theorem explainer
Local alias for the 4×4 matrix type already defined in the Regge continuum preflight layer. Gravity analysts cite it only to keep matrix notation unambiguous after several analysis modules are opened together. The body is a one-line abbreviation with no proof content.
Claim. Write $\mathrm{Mat}_4$ for the same 4-by-4 matrix type that the 4D Regge continuum preflight module already exposes, so that multi-module opens do not collide on the short name.
background
The parent module is the ledger-facing export for weak-field quadratic action recovery in the 4D QG campaign. It packages named closers such as the edge transverse-traceless decomposition and the claim that the recognition-mesh action converges to the Einstein–Hilbert quadratic form.
Several sibling analysis modules (edge TT decomposition, Regge edge stencils, exact flat Hessian symbols and Bloch/Rayleigh bridges) are opened together. Each may export short matrix or wave aliases. The continuum preflight module already fixes a concrete 4×4 matrix type used for discrete metric and Hessian bookkeeping; this abbreviation simply re-exports that type under a local short name.
No new continuum or curvature structure is introduced here. The surrounding campaign is restricted to weak-field quadratic action convergence, not sourced Einstein equations or full nonlinear continuation.
proof idea
Pure abbreviation: the name is bound directly to the preflight module’s existing 4×4 matrix type. There is no tactic block, no lemma application, and no computational content.
why it matters
Keeps matrix notation stable inside the export module that will eventually inhabit the two named Props (edge TT decomposition and SRS-to-EH convergence). Without the alias, multi-module opens risk ambiguous short names when Frobenius norms, wave norms, and Hessian symbols are stated side by side. It does not itself advance a forcing-chain step or close a gap; it is bookkeeping so that the later inhabitant of the action-recovery gap can be written cleanly. Downstream siblings that compare preflight Frobenius and wave norms to the identity rely on a single unambiguous matrix type.
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