Scheduling and pacing

The supplied ball-visit argument bounds:

1. moving ticks of one token in a fixed ball;

2. possible waiting sites for a leg pair.

Multiplying those bounds can introduce terms such as $L_m{w}_m/{\epsilon }_m$ or ${L_m}^2$, whereas the stated additive waiting estimate omits them. An injective charging argument or another uniform estimate is required.

Identical spatial carrier lines also do not force identical desired edges: two distinct desired edges can share an interior site and are not merged by a rule merging only equal edges. Their conflicts require a proof, including in dimension one.

The algebraic identity

follows from $\Delta t_m={\epsilon }_m/c$. The source's expression $w_m/(c{L}_m)$ is not the same identity. This arithmetic correction alone does not decide transport: the missing waiting and pacing proofs are separate.

The spatial lens/tube estimate controls where a path lies in space, not its time parametrization. Proposition prop:pacing shows why endpoint lateness is insufficient. Waiting at a destination can be far from the intended slowly moving spacetime wire.

For a general compact $K$, its fattening $(K{)}_{\rho }$ is not convex. For two widely separated points it is a union of disjoint balls, whose connecting midpoint lies outside it. Convexity of individual $d_c$-balls cannot justify arbitrary dwell segments inside that union.