IndisputableMonolith.Gravity.Analysis.EdgeTTDecomposition4DAudit
Audit shell for the 4D edge transverse-traceless decomposition of symmetric real matrices against a nonzero Euclidean wave covector. Gravity and QG workers cite it when checking that the algebraic W4-1 kernel stays consistent under the campaign's audit harness. Structure is import-and-reexport of the algebraic layer, not a new proof development.
claimModule-level audit of the linear-algebra transverse-traceless (TT) decomposition for symmetric $4\times 4$ real matrices relative to a nonzero Euclidean wave covector $k\in(\mathbb{R}^4)^*\setminus\{0\}$, as developed in the edge TT decomposition algebraic layer.
background
Recognition Science gravity analysis treats linearized curvature and stress response on a discrete recognition lattice. In the QG full-theory campaign (Wave 4, lane W4-1), the first kernel-checked increment is purely algebraic: decompose a symmetric $4\times 4$ real matrix into transverse-traceless plus residual pieces relative to a fixed nonzero Euclidean wave covector on $\mathrm{Fin},4$.
The parent module EdgeTTDecomposition4D supplies that algebraic layer. TT means the projected piece is orthogonal to $k$ in each index and has vanishing trace, the standard GR/spin-2 projector setup written over finite-dimensional real linear algebra rather than continuum PDEs.
This audit module sits one import above that layer. Its role is campaign hygiene: keep the W4-1 edge TT statements visible to the audit graph without adding new mathematical content.
proof idea
No independent proof development. The module imports the algebraic edge TT decomposition layer and exposes it to the audit harness. Any lemmas or definitions live upstream; this file is structural scaffolding for the Wave 4 campaign checklist, not a tactic or term proof.
why it matters in Recognition Science
Lane W4-1 (edge_tt_decomposition) is the smallest kernel-checked step toward a full quantum-gravity edge calculus in the Recognition monolith. Downstream gravity and QG assembly theorems need a certified TT split of symmetric $4\times 4$ data before curvature or propagator identities can be stated.
This audit module does not itself prove those identities. It pins the algebraic layer into the audit graph so regressions in the TT projector, residual complement, or wave-covector nondegeneracy hypotheses surface early. Parent consumption is currently empty in the graph (used_by count zero); the value is campaign bookkeeping for later 4D gravity analysis that will cite the algebraic decomposition.
scope and limits
- Does not prove continuum GR TT gauge fixing or PDE uniqueness.
- Does not introduce new TT identities beyond the imported algebraic layer.
- Does not treat Lorentzian signature or null wave covectors.
- Does not derive mass, alpha, or forcing-chain (T0–T8) claims.
- Does not assert downstream QG propagator or curvature theorems.