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Progress
Status: open / unregistered; realization material. Paper-derived research, not Established.
This page is the fixed-era instance: one settled semantics, one evaluator, no ontology revision. The canonical statement — the transport-weighted edge loss plus residual, bounded by three terms, on the accounted obligation state — is on Normative induction and Progress, and this instance is the edge bound with one era and one semantics.
"Progress" here does not mean the reasoner gets better at some task. It means something narrower and harder to fake:
A reason that stays live, is not answered, and recommends a specific available repair cannot be persistently ignored.
The failure mode it rules out is not error. It is behavioral inertness: the reasoner keeps the criticism on the books, keeps servicing it, keeps producing responses, and never actually changes what it does. Everything is recorded, the score is kept, and nothing moves.
Three inputs, and Progress is what happens when they compose.
Attention that does not run out. From the answerability side: a case that stays live receives unbounded cumulative attention. Diachronic Answerability delivers this and stops there, correctly observing that unbounded attention is not by itself improvement.
A reason-to-response structure. From Actionability: a live reason favours some available repair over recognizable non-response, and allocating enforcement intensity against a defect does a quantifiable amount of work.
Uptake. Something that prevents the pressure from being absorbed without effect. In the concrete construction this is the market maker's cumulative cap.
Put together: enforcement intensity allocated against a defect that persists must accumulate work, the cap bounds how much work can be accumulated, and therefore the defect goes to zero — at a rate that reads off the inverse square root of cumulative enforcement intensity.
Where Uptake comes from is a correction worth recording. The program believed for a while that it fell out of the underlying learning criterion for free. It does not: the enforcement position sits inside the price-setting aggregate and is not required to be efficiently computable, so the criterion never quantifies over it at all. Uptake comes from the market maker's cap, and the earlier claim was withdrawn.
There are two forms of the statement and they are genuinely different:
service-weighted Progress --Service Transport--> obligation-weighted Progress
the first being the learner-side mechanism theorem and the second the Answerability-facing endpoint.
"Progress" means the second. The learner-side theorem keeps its qualifier and is always service-weighted Progress, never the bare word.
Service-weighted Progress says the defect vanishes on the dates the reasoner worked. That is what the learner delivers, and it has a complete derivation with a rate — though like almost everything in this program that derivation is on paper and not in a proof assistant.
Obligation-weighted Progress says the defect vanishes on the dates something was owed. That is what answerability actually asks for. In the general theory the obligation measure is the special case of an externally declared evaluation measure over historical exposure; the learner does not get to choose it after seeing its mistakes.
The second does not follow from the first. A reasoner can drive its service- weighted defect to exactly zero at every horizon while its obligation-weighted defect tends to one half, simply by servicing the dates where nothing was wrong. Closing the gap requires Service Transport — an explicit accounting of which obligation, owed when, was discharged when.
The name went to the obligation-weighted form, and the tradeoff was taken knowingly: the transport interface and its residual are now inside the settled statement, so a Progress claim always carries a transport hypothesis. The alternative would have kept a cleaner theorem about a quantity answerability never actually asks for — which is the wrong thing to have a clean theorem about.
The obvious repair is a fairness requirement: over any long stretch, a decent fraction of service exposes a surface where this reason can actually be answered.
It is not enough, and the countermodel is embarrassingly simple. Two surfaces, one of which always has the defect and one of which never does, serviced in strict alternation. The fairness condition holds. Service-weighted defect is exactly zero at every horizon. Obligation-weighted defect tends to one half.
Of the four candidate interfaces the program considered for this, exactly one transfers: exposing a registered surface on every service date, with confidence bounded below. That gives a pointwise comparison between the two measures and the conclusion follows immediately. The others give the fairness condition and nothing more — and the countermodel is an instance of one of them.
It is not correctness. A reason may be wrong and the reasoner may respond to it perfectly.
It is not closure. Progress is about the trajectory, not about issues eventually being resolved.
It is not diachronic. Everything here is within one settled semantics, one evaluator, no ontology revision. Progress through a self-revision needs the content of a reason to be transportable across the revision — the semantic transport certificate that Diachronic Answerability assumes and the Normative Inductor lists among its open realization obligations.
Evidence. The schematic is
FINAL_SCHEMATIC.md;
the countermodel and the interface audit are in
SERVICE_TRANSFER.md
§3; the composition with rates is
FIXED_ERA_THEOREM.md.