service is allocated authority, not realized force

agent-decided, reversible. The reason-indexed service variable is the enforcement multiplier — equivalently the promised tolerance — chosen from the record through the previous date. It is not the realized position magnitude, which an earlier pass in this round had proposed.

Three failures decide it. The realized force is a function of the market maker's fixed-point price, so it is unavailable at the date the round's control must be chosen, and an affordability witness cannot be required to schedule it. It is zero exactly when the reason is perfectly satisfied, so its normalized measure does not exist on the trajectories the theory most wants to call well served. And it counts a date as better served because the reasoner did worse on it: equal allocated authority against violations of one tenth and nine tenths splits the force measure nine to one. A reason monitored forever at constant authority against a geometrically vanishing violation has divergent allocated service and summable realized force, so the realized reading classifies successful learning as starvation.

The control is correspondingly a predictable law from states to positions rather than a predictable position; in the traderized case the law must be continuous, which is what the fixed point's Brouwer step consumes. The affordability witness is retyped to (a_t, kappa_t) accordingly, with the realized control u_t = kappa_t(x_t).

Two things fall out. The per-date enforcement modulus already bounds the allocated-service-weighted squared violation, so service-weighted Progress is a consequence of the market maker's contract with an explicit rate rather than an assumed premise. And the liability charge grows like the square root of allocated authority, which is why a reason can receive divergent service on a finite lifetime budget: the market's own response reduces the force as compliance improves.

Rejected alternative: keeping the realized position magnitude as the service variable, which reads the schematic's scheduling freedom into a quantity no scheduler can set.