Abstract

We separate construction of a fixed-order interacting relational observable in a specified Einstein–scalar model from its matching to a specified ultraviolet candidate. The contribution is a self-contained collection of interface results. Pure-trace witness contractions do not determine a compact three-slot kernel, its free-shell class, or its microcausal admission; non-determination already occurs among smooth compact kernels. Density weighting retains preparation derivatives, and late source agreement does not imply agreement of retarded responses. We prove compact balanced-forest composition, reconstruction descent, conditional class-obstruction transfer, and coefficientwise separation of classical defects from positive formal orders in Planck's constant. For a completely specified affine Ward-normalization problem, exact cancellation is equivalent to vanishing in the quotient by the actual image of the admissible counterterm map. Finite probes, bounded normal order, and projected RG fixed points do not supply the corresponding unrestricted conclusions. Conditional assembly and continuum matching preserve a specified symmetry identity once their analytical hypotheses are supplied.

The operational framing distinguishes destructive classical readout from quantum-return decoding, complete preservation from subsystem recovery, and observable matching from spacetime or holographic reconstruction. Version-qualified comparisons with Cheung's manuscripts and a supplied OpenAI catalogue record are documentary constraints, not theorem premises. No complete gravitational characteristic coefficient, evaluated interacting one-loop observable, bulk BV restoration, or ultraviolet completion is established.