Technical audit of the formulation

The following points are part of the mathematical specification, rather than informal implementation assumptions.

1. One layer per tick. The support bound requires a partition layer. It would be false if arbitrarily many overlapping gates were allowed inside an uncharged tick.

2. One preparation per distinct site. Repeated route vertices are waits under the chosen monotone rounding convention. A fresh auxiliary is prepared at each distinct non-source site, not at every repeated occurrence.

3. Future-directed endpoint timing. The padded time (eq:null-construction), rather than the raw route time alone, ensures $T_j\ge T$. At most one padding tick is required for null targets.

4. Nontrivial payload dimension. The operational lower-bound and memory statements use $D\ge 2$. A trivial one-dimensional register cannot signal.

5. Complete versus reduced residual accounting. The ideal whole-output factorization (eq:state-invariant) is proved explicitly. Ignoring non-output factors does not mean that they were never initialized or retained.

6. Gate error versus full implementation error. Equation (eq:gate-noise) assumes exact preparations, spectators, waits, and output maps. Equation (eq:main-noise) is the complete-tick alternative. Small channel error alone does not establish causal containment.

7. Exact null attainment. Some finite-scale null pairs occur in this family. Proposition prop:exact-null characterizes them. The approximation theorem does not require their absence.

8. Restricted limit claim. The established limit compares endpoints and logical payload channels. It is not an unrestricted interpolation theorem, a global evolution semigroup, or a continuum observable-net limit.

9. Resource scope. The ledger includes initialized and retained quantum registers, the finite route description, and stencil permissions. It does not claim a physical energy, fabrication, or preparation-time budget.

10. Verification scope. The paper gives finite analytic proofs. No proof-assistant certificate, numerical execution, successful pdfLaTeX build, or laboratory realization is asserted.