Theorem: Boundary-to-interior conditional assembly

Fix one operational domain and one predeclared extraction package. Assume:

1. its event representation is faithful, spanning, and generated;

2. its constructed cone is proper, homogeneous, strictly convex, and has dimension at least three;

3. its probabilities satisfy Specification spec:boundary on a specified smooth coefficient class $\mathcal{C}$;

4. ${\mathsf{U}}_{\mathcal{C}}$ is independently established;

5. any identification between the affine event cone and a Lorentzian interpretation of the recovered Riemannian geometry is separately specified and proved;

6. any transport realization satisfies the complete-channel, endpoint, calibration, and resource hypotheses of Theorem thm:transport.

Then:

1. the represented cone is Lorentzian and determines a constant quadratic form up to positive scale on its affine carrier;

2. the operational boundary bank identifies $[g,A]$ in $\mathcal{C}$;

3. the supplied geometric interpretation has exactly its proved covariance and no stronger one;

4. the supplied finite protocols satisfy the complete-channel and endpoint certificate of Theorem thm:transport.

No Einstein dynamics, physical metric emergence, or inherited quantum-coefficient admission follows from these hypotheses alone.

Proof. Theorem thm:classification and Lemma lem:quadratic give the first conclusion. Theorem thm:boundary gives the second. The third follows only through the separately supplied identification; Propositions prop:signature and prop:lapse explain why it cannot be omitted. Theorem thm:transport proves the fourth.

The hypotheses include no independent source law or metric-jet dynamics. Propositions prop:flat and prop:conformal and the conserved-improvement example show why cone information alone cannot replace them. No hypothesis defines the separate characteristic quantum product.