Assessment 214: frozen support and current branching answers

12 October 2026. Written native construction 71 for a checked support-first subclass. Root admission and external priority remain separate.

Result and consequence

The complete argument supplies both producer and consumer. The initial consecutive row of the ordinary right relation builds a literal target support. Freezing it before other rows makes the branching coordinates stable. Later actual targets stream support-branch decisions into coherent row capsules and check a mixed-region budget against the common alias width. Every skipped unary symbol is still validated in the target query.

One pending row per source supplies exact immediate answers. The next actual alias pays the previous merge, including returns, observations and allocation; the new pending row cannot disturb an older unfinished job because that job has already completed. Unbounded right degree and arbitrary alias/target length ratios are admitted. The first-row support restriction, common target width, common alias width and mixed-region budget are checked gates, not promises or free decompositions.

This resolves the two immediate stress tests under the support-first premise. Long common stems no longer multiply selection work, and a complete cone is not fragmented by arbitrary context creation order. It does not permit late expansion of the support. Construction 70 remains a separate class: its bounded-degree dynamically learned contexts can admit targets outside the first row’s support. For example, records with alias/target pairs (0,000) and (1,111) pass its degree/class checks but fail construction 71’s frozen-support gate. Conversely, construction 71’s full-cube/half-cube family exceeds every fixed degree bound of construction 70.

Independent review and computational evidence

Independent adversarial review checked the initial conditional consumer, then the directly dependent producer, then the full written theorem. It confirmed that the fullness-cutoff proof uses a finite sequence of binary splits, not equal leaf depths. Feeding only actual support-branch events preserves its constant-view and no-return-walk contracts. The raw literal support trie supplies branch decisions without constructing compressed edges or doing pointer identity tests.

Review explicitly checked singleton support, a zero-length reduced code, the first unequal alias’s freezing deadline, later anchor duplicates, row and source ready writeback capsules, global budget-sign changes, intermediate violations that recover, empty factors, target-width mismatch and final negative answers. It required a separate literal validator: with support 000,111, routing 001 through the reduced tree alone can reach FULL incorrectly. Missing right support rejects the structural gate; missing pin support gives false product membership and therefore SAT.

The maintained Python audit contains one independently designed exhaustive core and the reconciled ordinary-record tests. It imports no other Lab checker. It passed:

• 391,272 exact merges and 3,127,536 committed-plus-pending queries over every nonempty support through literal width three and all pairs of row subsets.
• 35,220 support-relative insertions, including signed-budget identities and fullness at every changed coordinate, on nonuniform reduced trees and singleton supports.
• 1,200 seeded ordinary-record trials: 616 accepted, 584 rejected by the mixed-budget gate; 12,320 source updates, 24,640 retained-state checks and 149,760 pin checks.
• Explicit support-freezing, alias/target-width, malformed-record, duplicate-anchor, empty-factor and intermediate-budget-repair controls.
• Seven growing long-stem families and seven full-cube/half-cube families, checking branch-event counts and the absence of creation-order fragmentation.

Python sets, strings and integers are finite semantic oracles. These checks do not execute native dictionaries or the simultaneous-record compiler. The per-symbol and final-symbol resource bounds are supplied by the written construction and its inherited primitive contracts.

Six-result reassessment

Mathematical results 129 through 134 comprise the mixed-budget complete-level construction 66, sparse learned-spine construction 67, fixed learned-context construction 68, permanent-ownership construction 69, length-class refinement 70 and frozen-support construction 71. Their restrictions are not one monotonically expanding class.

Three mechanisms now have explicit paid implementations: coverage witnesses finish preparation; permanent ownership and compatible immutable codes keep contextual queries current; a frozen common support separates literal validation from branching union cost. The failure in assessment 213 explains why semantic injectivity alone cannot substitute for the last mechanism. These results move the investigation from storing a relation toward accounting for accessible current answers.

The general SAT/scaffold boundary is still open. None of these arguments joins independently owned arbitrary stores, converts arbitrary interfaces for free, or transfers entry 129’s growing-alphabet state/port lower bounds to a native language. Replay still pays its observations; affine fragment joins require their coordinate hypotheses; persistent causal algebra alone does not maintain a current union; unary coherent algebra alone does not provide branching readout. Compact storage is not a sufficient access-cost argument.

The next target is consequential and narrower than restarting the broad problem: allow one later support branch after many completed rows, keeping their old meanings and constant-time local child views. A support-relative FULL root can cease to be full when the support grows. Any repair must charge view conversion and budget updates before the next short selection and immediate query. Versioned support views or genuine later ordinary-input witnesses are plausible routes; the current argument does not establish either. There is no quota-based pause or campaign closure.

This result is classified as an extension of the Lab’s existing coherent-cutoff and asymmetric-splice proofs, with high confidence in that internal classification. The external ingredients remain those compared in section 32 and the dedicated reviews, most recently 210. No fresh primary-paper review or external originality claim is counted. The next scheduled assessment must complete both the substantive primary-proof review and editorial duties before it is counted once; preserve the exact mathematical next target during them.

Handoff and seven integration surfaces

Allow a later support expansion while preserving previously built row predicates, their mixed budgets and constant local child views. Begin with one added support branch after many completed rows and an immediate short-alias selection; charge old-view conversion to the expanding record or a proved later ordinary-input witness. Retain literal validation and current source semantics. Variable alias service widths, nested ownership holes, clipped intervals and independent-store joins remain separate.

Scheduled 118 to 119 and mathematical 133 to 134 are counted once. Six-result reassessment completed at 134, window reset to zero. Next scheduled 120 combines primary-proof review and editorial duties, counted once. Last completed dedicated review 210 and editorial 209 remain unchanged until those duties actually complete. Installed legacy reverse-writer retirement remains a separate unverified follow-up. No external messages.

Validation and publication

The scoped mathematical audit passed. Build, rendered mathematics/navigation/source checks, repository verification and exact saved-version/deployment/source-parity receipts belong to integration state. Publication is complete only with matching terminal deployment and parity evidence. Browser viewport inspection is unavailable under the supported Sites workflow; no viewport claim is made. Existing full-suite failures are not relabeled as successes.