Abstract

We give a self-contained local adaptation of Manuscript VI to the regular part of I-B's prescribed conical spacetime. On an explicitly supported developing presentation, we construct a second-order Einstein–scalar coefficient space and prove descent of a finite-time harmonic relational scalar under formal diffeomorphisms fixed near the initial surface. A constraint-compatible sourced family makes the construction nonempty and gives a strictly positive second-order relational coefficient.

The principal obstruction is retained rather than hidden by the adaptation. Replacing the scalar coefficient by a compactly switched retarded response produces an exact first-order gauge defect. A nested-support example has a normalized smeared gap at most $-1/2$, although the switch equals one near the entire observation. No correction beginning at second coupling order, or at positive $\hslash$-order, removes that classical gap while the lower-order prescription and identification are held fixed.

The additional contribution is an explicit finite certificate interface: three descended evaluations and the separate plateau-gap witness are encoded in finite diagonal matrices, read by a complete destructive-clock instrument, and transported with untouched references on a target-adapted causal route. Fixed-table approximation has a proved complete-channel limit. This combination may be useful as a reproducible separation between classical descent, switched compatibility, and operational readout; it is not a measurement construction for an unknown continuum field.

The local background, external schedule, initial-data prescriptions, and transport permissions are inputs. The regular cone is not globally hyperbolic, and the sourced example is not claimed to have compact metric Cauchy data. No intrinsic conical Green operator, quantum Ward identity, radiative response, or quantum renormalization separator is constructed. The quantum certificate remains RG-open.