Earlier paid contraction makes late answers accessible

13 October 2026. Written native construction 81 and its dependent short-key-map extension. A sufficient checked subclass, with no root admission or general lower bound.

For subsequent progress and the surviving frontier, see the current checkpoint. The targets below retain their assessment-date scope.

Result and contribution

The maintained proof closes the concrete escape test left by assessment 236. A sparse exchanged-leaf family had linear total routing but required too much freshly prepared explicit-path work before late selection. Two auxiliary activation indexes now remove that query-time work: actual activation records validate the long names and update their short varying keys. Growing independently prepared namespaces share these indexes and the original activation root.

One actual first foreign incidence learns the common shortening boundary. The theorem explicitly restricts that seed’s shape and placement; it does not supply a decomposition or assume arbitrary record-order invariance. Three constant query workers read the coherent current source tuple. The input’s final shape selects a ready answer, with exact original support preventing false shortened-key matches. Every worker’s release tails fit four normalized jobs per suffix symbol. Ordinary preparation also builds independently learned synchronous short-key maps, so the construction is not limited to one fixed suffix exchange in every namespace.

This is a written extension of the Lab’s existing capsule, provisional-lane, normalization and learned-routing methods. Sections 17–18 already supply constant alternatives, exact support and immutable commitment; constructions 78–80 supply alpha routing and paid replay. The additional content is their fully charged composition with an input-learned source-shared contraction. The old fixed-normalizer theorem and its bounded normalized degree do not directly imply this class. No separation from every previous native class or external priority is claimed.

The explicit family $n=2^\ell$ defeats every fixed construction-80 envelope-width contract but satisfies construction 81. This separates those sufficient contracts. It does not contradict the earlier mandatory-work cut, because the new representation reads prepared short predicates rather than traversing the long private owner paths. The catalog 129 state/port results, growing alphabet and matching/positive-path hypotheses remain unchanged; none becomes an unrestricted native lower bound here.

Evidence and seven-surface disposition

The standalone checker passed 5,460 bootstrap pairs, 2,048 exhaustive activation queries, 327,936 retained-version queries, 95,232 supported relation queries, 48,768 release schedules and 20 growing envelope witnesses. The dependent extension adds 60 prefix-conflict comparisons and 60 short-map activation queries. The explicit-transposition oracle is separate from the readout classifier; immutable roots are compared with saved activation sets. Release simulations check normalized jobs, not Python running time or native compiler execution.

Extension experiments sample complete prefix-tree automorphisms and conflicting duplicate rows, with the same sampled map in both lanes. They do not exhaust partial, noninjective or independently different lane maps. Those cases follow from the written prefix-consistency and actual-owner argument, not the experiment.

Independent adversarial review approved the base proof and dependent extension, including bootstrap timing, unary ruler construction, exact-shape commitment, coherent versions, release deadlines and the scoped comparison with old controls. The reviewer independently executed the final checker with identical counts. No blocking correction was required. One theorem and one substantive result are counted, not one per auxiliary lane or extension.

Current build, rendering, repository-suite and publication receipts belong to docs/integration/state.json and Git history. Passing finite checks does not constitute formal admission; no new primary-proof review is claimed at this assessment. The latest primary comparison remains assessment 235.

Continuation

Allow an input-built family of different exceptional suffix patterns while retaining a bounded number of source-shared indexes. Charge discovery and validation of their common representation, updates from literal owner names, and late query selection. Test whether a structural closure condition on the normalizers supplies a useful composition criterion. Independent synchronous maps on the already shared short keys are completed in construction 81. Preserve arbitrary whole-suffix permutations, arbitrary-name routing, cyclic sharing and heterogeneous service as open.

Scheduled completion 142 and mathematical 144 are counted once; native 81, window four, last reassessment 140. Next 143 is research; editorial 144 and primary 145 retain their separate cadence. All previous SAT/scaffold results and frontiers survive. Native recognition transfers only to the reversal of the complete checked language.