track1D_tt_projector_data_reduction_endpoint_holds
plain-language theorem explainer
Finite TT projector data on the N=5 periodic edge lattice is enough to close the Freudenthal conformal/gauge/TT orthogonal decomposition. Track 7 gravity handoff cites this as the Track 1.D receipt. The proof is a one-line application of the TensorShearSector lemma that builds the decomposition target from projector data.
Claim. For every gauge-potential type $G$ and every map from $G$ into periodic edge perturbations at $N=5$, the existence of finite TT projector data for that map implies the periodic Freudenthal conformal/gauge/TT orthogonal decomposition target at $N=5$.
background
This module is the Track 7 integration-lane receipt for parallel fork handoffs in the gravity master theorem. It records what each fork endpoint proves without upgrading the discovery claim; remaining Track 1 displacement-class leaves stay as open dependencies.
Track 1.D concerns the transverse-traceless (TT) sector on the periodic N=5 edge lattice. The endpoint proposition says: if one supplies concrete finite spanning-generator projector data (PeriodicTTProjectorData5) for a gauge map into PeriodicEdgePerturbation5, then the PeriodicFreudenthalTTOrthogonalDecompositionTargetAtN5 holds. That target is the conformal/gauge/TT orthogonal split used by the Freudenthal axis stencil at the forced spatial dimension D=3 (T8).
Upstream, TensorShearSector already packages the construction that turns projector data into the decomposition target; this declaration only freezes that implication as a named Track 1.D handoff fact.
proof idea
Term-mode one-liner. Introduce the gauge-potential type, the gauge map into periodic edge perturbations at N=5, and the projector-data hypothesis. Discharge the goal by exact application of TensorShearSector.periodicFreudenthalTTOrthogonalDecompositionTargetAtN5_of_projectorData on that hypothesis. No further rewriting or case analysis.
why it matters
Supplies the Track 1.D field of forkHandoffIntegrationCert, the integration-lane certificate that bundles Fork A–F receipts (Schläfli stationarity, physical residual/Bianchi, many-body amplitude lift, Page-capacity transfer, dark-energy w(z) band, falsifier sensitivity). Downstream doc: the cert "records exactly what the new endpoints prove."
In the RS gravity stack this closes the projector-data reduction leaf for the periodic Freudenthal TT split at N=5, tying the shear-sector analysis to the D=3 forcing (T8) and the eight-tick octave geometry. It does not finish Track 1: displacement-class stationarity leaves remain the next dependency flagged by the module doc.
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