Theorem: VII-E-ST local Grade S release

For the supported presentation and finite permissions specified above:

1. the observation contract has exact record and residual criteria, a robust residual obstruction, a sharp Lüders criterion, compatible continuations, restricted deferral, and its spectator theorem;

2. the hybrid contract has a complete state-independent branch representation, an intrinsic observation criterion, history closure, its own spectator theorem, and the whole-quantum-input recovery obstruction;

3. the four-face transverse family has explicit charts, edge laws, a compact collar, a supported $3+1$-dimensional lift, an exact event guard, and a decoder-correct finite reversible implementation;

4. the independent finite slice instrument has a certificate for every branch and changes no conical metric or worldsheet data;

5. the two-step model has the equal-slice residual separation and exact coarse-record channel gap (eq:exact-gap);

6. finite clock readout, residual audits, parameter compression, and reference-preserving causal transport are constructed on their stated finite interfaces.

These satisfy Definition def:grade. Neither source contract is used as an unproved premise of the other. The general interface results do not depend on the four-face illustration.

Proof. Theorems thm:pullback–thm:spectators-E give (i). Theorems thm:structure–thm:spectators-G, Theorem thm:decouple, and Corollary cor:informative give (ii).

Theorem thm:certificate gives (iii). Theorem thm:finite-model gives (iv). Proposition prop:equal-slice and Theorem thm:coarse-gap give (v). Sections sec:clock–sec:locality give (vi). All five defining Grade S interfaces have been specified.