affordability pays for the settlement-friction residual

agent-decided, reversible. On the sharp robust charge's linear branch the liability charge is computed from the supremum over live worlds of the same deficit whose service-weighted mean square is the settlement-friction residual. So the residual's numerator is exactly four times the charge, and a bounded lifetime budget with divergent allocated service drives the residual to zero — at the supremum world, not merely at the infimum the residual takes. The final claim-weighted defect is then bounded by the transport residual alone.

Once the learner can persistently afford a reason under the sharp worldwise certificate on that branch, the only remaining asymptotic error is how much the reason can change while waiting to be serviced. A corollary: on that branch a norm permanently excluding every live world by a fixed depth cannot be persistently and affordably enforced at all, so persistent affordable enforcement entails asymptotic compatibility with something still live.

The compression fails past the branch point, where the charge saturates and the numerator does not, and it fails exactly on the second route to cheap enforcement: a norm cheap because nobody trades against it buys persistence without buying conformance. Cheap enforcement is not always conforming enforcement, and which of the two routes made a date cheap decides whether Progress follows.

Rejected alternative: carrying the settlement-friction residual as an independent obstruction, which double-counts a quantity the liability budget already pays for.