Abstract

We study a new gauge-fixed Einstein–scalar application with constant gravitational and coordinate weights. Its action, field normalization, free Hessians, contraction kernels, quadratic gravitational source, observation root, and density map are specified consistently. An explicit marked response insertion produces seven distributional rows.

The revision separates these derived equalities from convention agreements and constant-weight specializations of supplied weighted formulas. A comparison panel displays the missing coordinate factors and density-weight derivative terms without adding an unproved weighted model to the main theorem. The cubic source is checked against an explicit Einstein–Hilbert density, and the action–stress signs, coupling powers, polarization factors, and symmetric-component conversion are recorded.

We prove row-by-row substitution, exact transposition to cone measures, and a 42-entry positive-scale audit identity. On the strict time-ordering patch, an exact crossed-line reduction and trace-reversal identity compress this ledger into a combined scalar-profile formula. The full eight-dimensional convolution is preserved, including for nonfactorizing profiles. All cone tips and source incidences remain in the internal distributional construction.

A conservative order-five estimate with scale power twenty-one is proved. This is not a leading asymptotic exponent. Neither the complete characteristic limit nor its failure is established. The application is not identified with an inherited weighted relational observable, and no quantum admission or gauge-invariant completion is asserted.