Mat4

The ambient module studies the genuine cross-term (directional) first variation of the exact midpoint Bloch symbol in the Euclidean weak-field transverse-traceless sector, then transports the torus-normalized continuum face by the banked continuum limit of the RS action on $H+K$ and $H-K$ together with polarization.

In that setting one needs a fixed matrix type for TT wave data, edge strains, Frobenius pairings, and coupling weights. The preflight continuum layer already fixes a $4\times 4$ matrix type for the closed 4D face; this module simply re-exports it under a short local name so later lemmas (pairings, strain linearity, coupling cross terms) stay readable.

Honesty constraints of the module still apply: the surrounding theorems live only in the Euclidean weak-field TT sector of the closed midpoint Bloch continuum face. They are not source equations, not Ricci or null focusing, and not GAP1 closure.

Definitional abbreviation only. The body is a one-line type synonym pointing at the preflight continuum $4\times 4$ matrix type; there is no tactic proof and no lemma application.

Gives the gravity analysis module a stable short name for the matrix carrier of TT data on the closed 4D continuum face. Downstream siblings in the same file (wave data, Frobenius pairing, edge-strain linearity, coupling cross weights, and the exact midpoint Bloch first variation) all sit on this carrier.

In the broader Recognition chain this is scaffolding notation inside the Euclidean TT first-variation layer that feeds the banked continuum transport toward Einstein–Hilbert structure. It does not itself touch T0–T8, the Recognition Composition Law, or the missing Freudenthal exact-$J$ metric refinement that would identify sourced response with the midpoint variation.