claimroutine

Fresh presence tests before value or motion

Fresh presence tests before value queries keep the ad+b(t−j)ad+b(t-j) bound
shows entry wrappers add no control overhead
Claim·§11.4 Certificates for the estimator recipes·inside lemEstimator recipes have regenerable records and bounded control

Statement (paper)

Every entry wrapper that tests presence, class membership or outer validity before a value query or motion can be placed a fixed number of strata above its validity predicates and value or motion cores, so that its structural test is called at clock zero with O(d)O(d) retained descriptor and control bits and its boundary is bounded by O(d)+btO(d)+bt. After the test finishes, only bounded status and descriptor data remain, so a subsequent call to a numerical core at clock jj has boundary at most ad+b(t−j)ad+b(t-j) after enlarging aa. These wrappers preserve the represented relations, values and outgoing endpoints, and the predicates do not call the score, gate, cap, new bucket or new shortlist whose value is being checked.

In plain English

Entry wrappers that test presence, class membership or outer validity before a value query or motion can be placed a fixed number of strata above their validity predicates and cores. The test is called at clock zero with O(d)O(d) retained bits and boundary O(d)+btO(d)+bt, and a later call to a numerical core at clock jj has boundary at most ad+b(t−j)ad+b(t-j) after enlarging aa, while the represented relations, values and endpoints are preserved.

Why it's here

This step of the lemma 11.10 proof shows that checking presence or validity first does not inflate the control bounds. The test runs fresh at clock zero and leaves only bounded status and descriptor data, so the later value or motion call inherits the stated ad+b(t−j)ad+b(t-j) bound. The predicates never call the score, gate, cap, new bucket or new shortlist being checked, so no circular dependence arises, and the exposed classes and restoring paired motions from the atom-margin, cap and ordered-path lemmas supply the tests and motions the wrappers use.
Classified routine:
Bookkeeping step inside the proof of the estimator-recipes lemma: it places the presence and validity tests in fixed strata and checks the space and boundary accounting, using the exposed classes and restoring motions supplied by the atom-margin, cap and ordered-path lemmas.

Uses

lemAtom margins: sparse rows with exposed classeslemCapped incoming ports give restoring paired motionslemUnbalanced estimator paths have ordered restoring form

Used by

Nothing in the paper

Sources

PaperOpen
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§11.4 Certificates for the estimator recipes
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sections/implementation.tex:906
Leannot aligned

Phase 2 aligns this node to a Lean declaration.