Abstract

Track A seeks a renormalized relational observable on a fixed external-time background. This first artifact does not announce that quantum construction. It specifies an independent original-rod lapse prescription on an explicit on-shell power-law Einstein–scalar background and proves its complete classical expansion through second perturbative order.

The clock calibration, positive lapse branch, slice-harmonic rod equations, spatial boundary condition, perturbation convention, and gauge group are fixed before calculation. The second spatial rod is constructed, and its absence from the quadratic lapse is proved. An explicit compact perturbation distinguishes the original rods from lapse-weighted modified rods. The complete linear observable and quadratic Hessian satisfy a coupled classical gauge identity; the Hessian alone is not declared linearly gauge invariant.

We also isolate the instantaneous kernel and spatial-tail issues that a quantum construction must address. A regularized polynomial has a conditional finite-order Wick realization once contraction data are supplied, but this fact does not construct the unsmoothed lapse. An exact affine Ward-repair criterion is proved without assuming that its target breaking or counterterm images have been calculated.

The native quantum milestone remains unresolved at Q1: a complete coupled gauge-fixed realization, Green distributions, and normalized contraction data have not been supplied. No retained-order quantum Ward identity, regulator removal, inherited characteristic quantum coefficient, external-time-free evolution, or compilation is asserted. All predecessor comparisons retain declared path null, and the standing insertion, route, and admission boundaries are unchanged.