Premetric Structural Unification: From the AASC Kernel to Einstein-Form and Free-Scalar Dynamics

What the paper constructs

The construction instantiates Kernel governance, AMetric authority restrictions and canonical L-metric licensing on actual original-use tasks. Concrete downstream constructors supply the physical parameters, carriers, action and analytic hypotheses. The licensed receivers preserve the declared readouts and continuations.

The metric branch connects the original Einstein–Hilbert action-derived source to its same-current-metric representation and Einstein-form response classification. The free-scalar branch supplies the exact Schrödinger generator, complete weak operator graph/domain and a calibrated comparator theorem.

A common-preparation map preserves the original one-particle-core preparation, independently admitted metric operand, complete original records and registered answers. Its evolved version retains the stated scalar-core evolution. The composed Lean root has 49 proved fields, with connecting maps and coverage rather than an inference from shared imports.

Scope and dependencies

The result is a completed premetric structural unification within the declared bounded EH and free-scalar constructions. Structural emergence means dependency and derivation within those constructions. It retains metric-admission hypotheses, nonzero EH coupling, the controlled nonrelativistic step and comparator calibration; it does not claim branch-quotient identity, a preferred projection, coupled Einstein–scalar dynamics or unrestricted candidate exhaustion.