Assessment 193: a local frontier removes the suffix name gate

10 October 2026. Written native theorem 61; finite immutable audit; no root admission or external novelty priority claim. 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 proof removes the exponential name/minimum restriction for right-first suffix rows with a common maximum. The new worker needs no general priority queue: new jobs enter age zero, each observed digit promotes one age, and a completed minimum discards all higher ages. Unary gap roots make every structural change local to the head and its successor.

The investigation first developed a joint dyadic screening/reduction contract. Its idealized audit checked the work envelope while retaining a priority oracle. Deep-directory repair and stale replacement failed. The sparse representation then removed that oracle and the deep repair. Its final simplification promotes after every digit, eliminating the geometric scheduling counter as well.

The sparse-age checker uses explicit immutable buckets, unary ages/gaps, job stacks and digitwise comparisons. It checks 8,450 invariant states, 800 retained forks, 5,600 completed-minimum answers, 93 comparison interruptions and 12,800 query-prefix answers with lag repair. A 50,001-bit pending numeral followed by endpoint 2 is also checked. A separate deep-frontier test builds eleven simultaneous buckets and checks 600 interruption forks before promotion and reduction. The final worker has no arithmetic counter, priority selector or endpoint-order oracle. Original unary reader lengths and lag repair are modeled arithmetically in the audit; right-input production and the scaffold compiler retain their inherited proofs. Finite checks corroborate the written all-length argument.

The proof was reviewed against four failure points: a promotion into a suspended comparison preserves its minimum; a lower completion deletes only dominated higher ages; empty bucket removal cannot create an unbounded scan; and the query worker needs only an idle-head test, with no rank comparison or coverage oracle. All endpoint-order tests use observed digits. The constants are fixed independently of the input and all work is paid after its own release.

This is an extension of the Lab’s existing counter, dictionary and reader constructions. Comparison-based heap theorems assume completed comparisons; the new specialization schedules those digits and uses adjacent promotion plus upper-tail deletion. No general heap improvement or literature-priority claim follows. Common maximum and suffix shape remain substantive gates.

NEXT: Test two final maxima for suffix rows. A row with the smallest minimum may end before another row begins, so deleting all larger-rank candidates is no longer sound. Construct a paid coverage frontier or give a precise obstruction; charge classification, lower/upper endpoint work, version preservation and final-symbol readout. General interior intervals and independent-store joins remain separate.

Scheduled completion 98 counts this assessment once. Substantive mathematical count 124 and six-result window two advance once for theorem 61; reassessment 122 is unchanged. Next 99 is research, literature review 100 and editorial 102 remain due. Source, evidence and failures are maintained in GitLab; the public projection uses styled proof and highlighted code readers with exact downloads. Verification and publication receipts are in integration state.