The supplied gravitational scalar records are not this example

Em02-E's lapse is a relational metric quantity on a declared Einstein–scalar background. Its reported second-order coefficients include clock and spatial-rod corrections CheungEm02E. They are not $L=-Q/2$.

Em03-A's scalar lives on a fixed normalized Schwarzschild exterior, with its specified state and radial scattering problem. Its reported surface gravity is $\kappa =1/(4GM)$, and bulk Unruh identification is an external input in that manuscript CheungEm03A. Those geometry and state data are not the Minkowski example.

A local equivalence of field equations in one coordinate patch would not identify the states, local algebras, horizon geometry, or complete channels of the two constructions. No such identification is supplied here.

The chiral circle-net correspondence reported by Family 280 is a different dimension and framework; the preceding Oai280-A draft retains it as a source record Oai280A,Dossier. Family 211's planar-map and metric-measure limits and the Oai211-A comparison likewise do not supply this four-dimensional Ward identity Oai211A,Dossier.