Track1DTensorShearScaffoldIntegrationEndpoint
plain-language theorem explainer
Integration-lane alias of the Track 1.D tensor/shear scaffold: edge-level perturbations carry the sector, and nontrivial rectangle shear is not vertex-conformal. Gravity Track 7 cites it when packaging fork handoffs into the master integration certificate. The body is a one-line re-export of the TensorShearSector endpoint Prop.
Claim. The Track 1.D integration endpoint is the proposition that (i) every 3D triangulation admits a map from vertex potentials to edge perturbations, (ii) the length-5 encoded edge-perturbation space is equivalent to the periodic edge-perturbation space, and (iii) whenever two real edge values $h \neq v$, no four real vertex shifts realize those values as mid-edge averages in a vertex-conformal way (nontrivial rectangle shear is not vertex-conformal).
background
Module MasterTheoremHandoffIntegration is the Track 7 receipt for parallel fork handoffs (Tracks 1.B–1.C, 2.C, 3.C, 4.C, 6). It records what each new endpoint proves without upgrading the discovery claim; remaining Track 1 displacement-class leaves stay open.
Track 1.D lives in the tensor/shear sector. The upstream scaffold endpoint packages three facts: existence of a carrier map sending vertex potentials on any 3D triangulation to edge perturbations; an equivalence between encoded and periodic length-5 edge perturbations; and a rigidity statement that nontrivial rectangle shear cannot be realized by vertex-conformal mid-edge averages when the two edge values differ.
This declaration simply names that same proposition in the integration lane so Fork handoff certificates can consume a stable local symbol.
proof idea
Definitional one-line wrapper. The Prop is definitionally equal to TensorShearSector.Track1DTensorShearScaffoldEndpoint; no extra conjuncts or proofs are introduced here. Inhabitation is proved downstream by track1D_tensor_shear_scaffold_integration_endpoint_holds, which applies the upstream track1D_tensorShearScaffoldEndpoint_holds.
why it matters
Gives Track 7 a named handoff for Session 215 Track 1.D: edge perturbations are the right carrier for tensor/shear work, and nontrivial rectangle shear is not vertex-conformal. Downstream, ForkHandoffIntegrationCert consumes the fork endpoints as stronger handoff facts while keeping the structural master theorem on structural witnesses; the companion theorem track1D_tensor_shear_scaffold_integration_endpoint_holds discharges this Prop. It does not close open Schläfli or displacement-class leaves; those remain the next Track 1 dependency. In the gravity stack this is interface packaging, not a new dynamical law or a forcing-chain (T0–T8) step.
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