Results and dependencies

The main results are:

1. exact finite-step support containment and causal-cut factorization for prescribed channel dynamics;

2. retiming invariance for a fixed labelled gate partial order;

3. spectator-extension invariance under complete control and resource blindness;

4. restricted destructive deferred-readout equivalence;

5. an effect-pullback criterion and exact unassisted record error;

6. a residual-instrument obstruction and accessible-algebra comparison criteria;

7. a complete fixed-spacetime certificate for one four-face adjacency exchange.

Supplementary interface propositions give complete-process record laws, a classical-register memory witness, and conditional approximation and sampling bounds.

Finite-dimensional channel conventions follow Watrous Watrous2018. The circuit precedent for deferred measurement is Gurevich and Blass GurevichBlass2022. The geometric setting uses conical point-particle spacetimes and polygonal developments DeserJackiwHooft1984,tHooft1992, tHooft1993,Kadar2005.

Cheung's companion records motivate comparisons with observation, process, and schedule interfaces CheungVIIE,CheungVIIJ, CheungPsy02A,CheungPsy02B. They are not premises transferring a model identity or a gravitational solution. Every mathematical statement used here is formulated and proved locally. The source ledger in app:sources distinguishes full supplied passages from statement summaries; no inspection of an entire manuscript corpus is claimed.