Theorem: Finite observation-compatible model

The model (eq:labels)–(eq:model-branches) has:

1. state-independent completely positive trace-preserving hybrid evolution;

2. a certificate for every nonzero branch, without postselection;

3. source-sensitive successor probabilities for $\eta >0$ and nontrivial coherent feedback for $0<\eta <1$;

4. branchwise population-observation closure, complete history laws, and spectator consistency;

5. full-instrument-equivalent immediate and locally deferred implementations;

6. exactly $\min \{n,B-k_0\}$ source attempts after $n$ hybrid ticks, one permission per attempt, and at most $B-k_0$ retained outcome bits.

The cone, deficit, worldsheet, and peripheral affine gluing are unchanged.

Proof. Completeness and Theorem thm:structure prove (i). Lemma lem:slice-certificate proves (ii). The explicit effect and phase formulas prove (iii). Theorems thm:histories and thm:spectators-G apply to the diagonal branch matrices and blind fixed controller, proving (iv). The pointer calculation proves (v). The resource $B-k$ decreases once per active branch and no attempt is made at $k=B$, proving (vi).