Track1DTTHessianLichnerowiczEncodedCoeffRelativeTranslatedDiagnosticEndpoint
plain-language theorem explainer
Defines the Track 1.D diagnostic endpoint as an implication: any relative-frame translated TT-Hessian/Lichnerowicz coefficient certificate yields a nonempty origin-column formula package. Gravity auditors cite it when wiring Fork handoffs into Track 7 without claiming the full absolute translated row formula. The body is a pure Prop abbreviation, not a proved theorem.
Claim. The Track 1.D diagnostic endpoint is the proposition that every relative-frame coefficient-only translated residual formula datum (Regge Hessian and lattice Lichnerowicz kernels, residual displacement coefficients, and the relative entry formula) implies that the corresponding origin-column formula data package is inhabited.
background
Module context is Gravity Track 7 fork-handoff integration: receipts for parallel forks (Schläfli stationarity, physical residual/Bianchi, many-body amplitude lift, Page capacity, $w(z)$ bands, falsifier sensitivity) without upgrading the discovery claim.
In the tensor-shear sector, the relative translated formula data records that generated physical stencils are translation-covariant after each row is re-based at its own edge base. That surface is deliberately weaker than an absolute translated certificate for every row.
The origin-column package keeps only the part of a relative certificate that agrees with the existing origin-row generator map: the same kernels and residual coefficients, plus an origin-column entry formula. Track 1.D asks only that the relative certificate expose this shared origin-column consequence.
proof idea
No proof: this is a definitional Prop. It is the function type from relative-frame translated coefficient formula data to nonempty origin-column formula data. The companion theorem track1D_..._endpoint_holds later discharges it by intro on the relative datum and packing ofCoeffRelativeTranslatedData.
why it matters
Track 7 consumes this endpoint as a diagnostic handoff, not a closure of absolute translation. Downstream, ForkHandoffIntegrationCert and fork_A_B_C_D_E_F_handoffs_integrated_one_statement bundle it with Schläfli reductions, physical residual interfaces, many-body lifts, Page capacity, $w(z)$ bands, and falsifier sensitivity, while explicitly refusing the unconditional discovery theorem.
The doc-comment states the design: physical stencil covariance still must be converted into an absolute row formula or a shifted-generator theorem. That keeps Track 1 displacement-class leaves open as the next dependency, matching the module's integration-lane role rather than a master-theorem upgrade.
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