Wave4
plain-language theorem explainer
Local alias for the four-dimensional wave (test-variation) carrier from the Regge continuum preflight. Gravity analysts working the Recognition-mesh exact-J bridge cite it whenever they need the preflight wave type without a long qualified path. The body is a one-line abbreviation with no proof content.
Claim. Write $\mathrm{Wave}_4$ for the type of four-dimensional continuum-preflight wave modes (amplitude test variations) already fixed in the Regge 4D preflight layer; this declaration is only a local name for that type.
background
The host module builds the canonical Recognition mesh on the periodic Freudenthal 4-torus and attaches a value-level action whose amplitude Hessian is the geometric Option-C midpoint Bloch symbol. Preferred limit shape is amplitude Hessian at fixed mesh, then mesh refinement $N\to\infty$.
In that setting a wave is a discrete test variation on edge classes at amplitude $\varepsilon$. The preflight layer already packages the 4D wave type together with norm identities and pullback exclusions; the present module only needs a short local name for that carrier when it defines mesh waves, true-Regge quadratic Hessians, and the exact-$J$ action on the mesh.
Binding honesty in the module doc keeps the Regge identification at MODEL level: elevating the Hessian to the full nonlinear Regge action via Schläfli stays open, and the construction does not consume amplitude-scaling refinement families as continuum premises.
proof idea
Definitional one-line abbreviation: the name is bound directly to the preflight module's four-dimensional wave type. No tactics, no lemmas, no computational content.
why it matters
Keeps the Recognition-mesh exact-$J$ bridge readable while it wires mesh waves to the Option-C midpoint Bloch symbol and the true-Regge quadratic Hessian. Downstream siblings in the same file (mesh wave, exact-$J$ action on the mesh, equality of that action with the true-Regge Hessian, and the continuum $N\to\infty$ Tendsto to the scale-explicit Einstein-Hilbert face) all speak in terms of this carrier.
Inside the QG full-theory campaign this sits at the Recognition gate of 4D continuum closure. It does not itself close gap-action recovery or inhabit the full $S_{\mathrm{RS}}\to\mathrm{EH}$ convergence statement; those remain separate obligations named in the module doc.
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