Gravity Analysis Edge Ttdecomposition Closer4 D Edge Tt Decomposition Holds

The edge decomposition

In general relativity, gravitational waves are often analyzed by splitting the metric perturbation into transverse-traceless (TT) parts, the physical wave degrees of freedom, and gauge parts, which carry no physical information. The Recognition Science declaration edge_tt_decomposition_holds establishes, as a proved theorem in the framework's machine-checked library of formal theorems, that this split exists for the framework's discrete ledger model of spacetime edges. Specifically, it proves that any wave mode with nonzero momentum can be decomposed into an algebraic TT part, plus normalized plus and cross polarization witnesses, plus a pure-gauge non-transverse decoy that drops out of physical predictions.

The theorem is a named closer, meaning it assembles previously proved pieces: the algebraic TT decomposition, the Frobenius-normalized polarization witnesses, the decoy gauge field, and the plane-wave edge attachment already proved in the framework's Regge edge theory. The decoy is shown to be non-transverse, so it cannot be mistaken for a physical wave mode. This is the algebraic and attachment layer of the framework's gravity analysis; it does not yet recover the full continuum theory.

In Recognition Science, the framework models spacetime as a discrete record of recognition events, a ledger, and derives physical laws from the cost of maintaining that record. This theorem is a step in that program: it shows the ledger's edge structure supports the same kind of wave decomposition that continuum general relativity uses. The full recovery of the Einstein-Hilbert action from the ledger remains an open target, gated behind the declaration S_RS_converges_EH_4d.

What the theorem does not claim: it does not prove that the framework's discrete ledger reproduces all of general relativity, nor that gravitational waves in the ledger propagate exactly as in the continuum. It establishes the algebraic decomposition and attachment layer only. The full multi-orbit true-weight continuum recovery is not part of this declaration.

theorem edge_tt_decomposition_holds :
    Regge4DContinuumPreflight.edge_tt_decomposition :=
  edge_tt_decomposition

theorem decoyGauge_not_transverse :
    ¬ IsTransverse axisWave decoyGauge := by
  rw [decoyGauge_eq_decoyLongitudinal]
  exact decoyLongitudinal_not_transverse

What this page does not claim

This theorem does not prove that the framework's ledger reproduces all of general relativity. This theorem does not establish the full continuum recovery of the Einstein-Hilbert action, which remains an open target. This theorem does not claim that gravitational waves in the ledger propagate exactly as in the continuum theory.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Gravity/Analysis/EdgeTTDecompositionCloser4D.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

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