track1D_tensor_shear_scaffold_integration_endpoint_holds
plain-language theorem explainer
Track 1.D records that edge-level perturbations are the right carrier for tensor/shear work and that nontrivial rectangle shear is not vertex-conformal. Gravity Track 7 cites this when assembling the fork-handoff integration certificate. The proof is a one-line re-export of the TensorShearSector scaffold endpoint.
Claim. The Track 1.D tensor/shear scaffold endpoint holds: edge-level perturbations are the correct carrier for tensor and shear analysis, and nontrivial rectangle shear is not vertex-conformal. Equivalently, transverse-traceless structure is represented by finite orthogonality to the periodic conformal slice together with a caller-supplied gauge slice.
background
This module is the Track 7 integration-lane receipt for parallel gravity fork handoffs. It does not upgrade the discovery claim; it records exactly which new endpoints hold and leaves remaining Track 1 displacement-class leaves as the next dependency. Fork packaging spans Schläfli stationarity, physical residual/Bianchi, many-body amplitude lift, Page capacity, dark-energy $w(z)$, and falsifier sensitivity.
Track 1.D is the tensor/shear scaffold leg. In the Recognition geometry, spatial dimension is forced to $D=3$ (T8/T9). Continuum identification equates a weighted edge Laplacian on vertex defects with a hinge-area curvature sum, so edge-level carriers are the natural place to host shear. The scaffold asserts that nontrivial rectangle shear fails to be vertex-conformal, so TT work must live on edges rather than pure vertex conformal modes.
Upstream, the periodic Regge TT geometry assigns hinge-aware zero modes cell-independently; the scaffold endpoint packages that setting into a Prop consumed by the integration certificate.
proof idea
One-line term wrapper. The integration endpoint is definitionally the TensorShearSector scaffold endpoint Prop, and the proof applies TensorShearSector.track1D_tensorShearScaffoldEndpoint_holds with no extra hypotheses or rewriting.
why it matters
Track 7 needs a single inhabited certificate that every fork handoff endpoint is discharged. This theorem fills the Track 1.D slot of forkHandoffIntegrationCert, so the integration lane can truthfully claim the Session 215 tensor/shear scaffold is in hand.
In framework terms it sits downstream of the $D=3$ forcing and the simplicial-to-continuum edge Laplacian bridge: shear is forced off the vertex-conformal slice onto edges. The accompanying comment is explicit that TT is only represented as finite orthogonality to the periodic conformal slice plus a caller gauge slice; constructing the actual projectors remains the next tensor-sector proof. That is the open leaf this endpoint deliberately does not close.
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