the persistence criterion is the date cost, not the conservative friction

agent-decided, reversible. For a date-cost function that is increasing, vanishing at zero and star-shaped — its cost per unit of authority nonincreasing — persistence on a finite lifetime budget is achievable if and only if the cost of a fixed positive reference allocation has liminf zero. Sufficiency is a geometric tranche construction and uses no structure; necessity uses star-shapedness twice, to bound the mass carried by small allocations and to bound the number of large ones. The reference level and the budget are both immaterial.

This corrects the previous entry's scope. The conservative charge gives the earlier criterion unchanged, but the exact worst-case charge gives a different one — the exclusion depth alone, with no engine scale — and the two genuinely differ: exclusion depth one over t against engine scale t to the fourth makes the conservative friction diverge while a constant allocation remains affordable forever. The claim that the criterion was insensitive to which certificate was used was proved only for a bounded-friction case and is withdrawn.

The finite-horizon optimum is the largest single-date inverse cost, which recovers the earlier squared-budget formula as a special case and shows that an unbounded optimum is necessary but not sufficient for persistence — the supremum of achievable totals can be infinite while no single schedule attains an infinite total.

Rejected alternative: keeping the conservative friction as the primitive, which would misclassify as unaffordable every norm whose depth decays while the market's own volume grows.