persistent enforcement is affordable iff the friction dips to zero

agent-decided, reversible. Write the friction of a normative row at a date as its worst live exclusion depth times the square root of the date's slack-plus-volume. A schedule with divergent cumulative allocated authority and finite lifetime worst-case charge exists if and only if that friction has liminf zero, and the maximum cumulative authority through any horizon is exactly the squared budget over the squared running minimum friction, attained by putting the whole budget on a single least-friction date.

Three consequences are adopted with it. Persistence is budget-free — the criterion does not mention the budget, so any positive lifetime budget buys it and none buys it when the friction is floored. Persistence does not compete across reasons, so splitting one budget geometrically serves every individually persistable reason at once and there is no Hall-type condition to look for. And a causal scheduler seeing the friction only at its own date achieves persistence exactly when an offline one can, by a doubling-threshold rule; any scheduler with a positive floor on its per-date allocation is defeated by a friction bounded away from zero, so persistence requires the freedom to do nothing.

The reading is that a norm can be enforced indefinitely on a finite liability budget exactly when there are infinitely many occasions on which enforcing it is nearly free. That pushes the burden onto transport stability across the resulting gaps, which is where affordability and service fidelity now pull against each other.

Rejected alternative: an l^p or summability condition on the friction sequence, which is sufficient in the l^2 case and nowhere near necessary.