Assessment 192: screening debt and the missing persistent frontier

10 October 2026. Sustained unsuccessful native construction attempt. Conditional scheduling argument and finite experiments; theorem 60 and root claims unchanged. This is a dated assessment record.

Current continuation: The composition checkpoint records the live target. Ordered suffix reuse is the strongest completed suffix construction, covering every fixed final maximum diversity. Historical next tests and counts below retain their assessment dates.

The complete attempt separates endpoint screening from completed-minimum aggregation. Giving priority to the least-observed endpoint bounds the remaining work through any fixed digit depth using only distinct ordinary-name arrivals. It escapes the two required adversaries in the abstract model. The scheduler’s priority choice and the completed-set answer remain explicit oracles, so this does not remove the native theorem’s name/minimum restriction.

The attempt also rejects newest-only preemption: a newer enormous task can bury an older small endpoint. A literal immutable age-bucket chain requires copying an unbounded prefix to update a deep bucket; retaining a separate finger leaves the original root stale. Epoch suspension avoids inspecting certified-large groups early, but naive concatenation defers an unbounded traversal. Finally, an old comparison can overwrite a newer smaller answer unless the pending reduction is version coherent. The note records the exact contracts and reopen gates, rather than claiming a native lower bound.

The Python screening audit checks 11,480 release prefixes, 249,248 debt inequalities, 2,700 retained forks and 8,100 threshold memberships. A late endpoint 2 and 1,025 distinct equal-small completions pass. Eight symbolic newest-only witnesses, a stale-commit witness and 509 phase inequalities are checked. Tuple scans, integer priorities, bit-length exhaustion and completed-set scans are semantic oracles, explicitly excluded from the native cost claim.

NEXT: Implement a persistent epoch frontier with certified lower bounds on suspended groups and a version-coherent pending minimum reduction, without a free minimum-age selector, uncharged bucket repair or free catenation. First charge a merge after many low-age interruptions and a late small completion during an older minimum comparison. Establish joint linear work through each digit-depth cutoff, including scheduler, reduction and reader repair, before every query deadline, or give a precise failing history. Retain the late-small and unbounded equal-small tests; general intervals, varying maxima and independent-store joins remain separate.

This is a work-distribution diagnosis and implementation attempt, with no new native recognizer, scientific admission or novelty claim. The strict FIFO, replay, affine, causal and unary coherent controls retain their original interfaces; none grants a free growing priority frontier. Primary entry-129 theorems retain their matching and positive-path hypotheses.

Scheduled completion 97 counts the assessment once. Mathematical count 123, window one and reassessment 122 remain unchanged. Next 98 is research; literature review 100 and editorial 102 remain due. Source and computational evidence are retained in GitLab. Public publication is deferred until the paid frontier and reduction make a coherent advance or the failure yields a decisive broader boundary; future publication must use the generated HTML/KaTeX and highlighted exact-download readers. Existing public theorem 60 remains intact. Verification and publication dispositions are recorded in integration state.