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Item 76: Certify a reason's temporal modulus

Deference line — second wave · difficulty entry · project normativity · open · node item-76

The canonical Sharp Timely Service bound ends in a single term: the obligation-normalized semantic error incurred while a reason waited to be answered, bounded by the reason's temporal modulus at the plan's delay. The round has no mechanism for establishing that modulus for any reason, which means the theorem's conclusion is exact and its last constant is a symbol.

Settle what a modulus certificate could be. The deductive channel is the place to look: if a reason's defect is a function of the settled record and the record grows by a bounded amount per date, the modulus is a property of that dependence rather than an empirical estimate. On the empirical channel a funded procedure can settle within the window and move the depth arbitrarily, so it is plausible that no modulus exists there and the honest form is a conditional statement.

Deliverable shape: a stated theorem with exact-rational fixtures, or a demonstration that the empirical channel admits no modulus. Acceptance check: the round's runner is discovered by python3 tests/run.py and passes.

Context: projects/normativity/legitimacy/rounds/2026-08-31-normative-affordability/SHARP_TIMELY_SERVICE.md for the theorem and hypothesis (T), SERVICE_TRANSFER.md for the normalized transport error the modulus bounds, and CLOSED_LOOP_EXISTENCE.md §3 for the deductive and empirical channel split. A solution ships: the certificate class, and what Answerability has to export for it to be checkable.

Deliverable shape: a stated theorem with exact-rational fixtures, or a demonstration that the empirical channel admits no modulus.

Acceptance check: the round's runner is discovered by python3 tests/run.py and passes.

Context: projects/normativity/legitimacy/rounds/2026-08-31-normative-affordability/SHARP_TIMELY_SERVICE.md

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