Shared contexts make residual answers affordable

12 October 2026. Assessment 207, scheduled completion 112. Written native construction 68 extends the existing pending-word mechanism by learning a fixed number of shared target prefixes from ordinary input. The complete argument is the maintained proof.

Later development: review 208 permits unbounded separated groups under a checked common-route restriction. It does not resolve the unrestricted learned hierarchy.

Result and payoff

Rows may have arbitrary ordinary-name aliases and an unbounded collection of different target parents. For fixed context count, row degree and residual length-class span, actual input learns shared prefixes; selections update current residual predicates; queries check each shared prefix and start its residual reader at the correct input position. Final negative answers require no flush.

This handles assessment 206’s unchanged long-stem sibling-pair family, including arbitrary permutations between short aliases and suffixes. It avoids the failed dispatcher’s separate full-stem traversal for each selection. It does not solve unrestricted aliases: admission uses a deterministic, order-sensitive context rule and bounded residual span. The theorem 67 learned-spine construction remains a separate positive control; neither construction is claimed to subsume the other.

Construction and actual-draft review

The first record needing a new context retains a rolling FIFO of its final |v|+1 target bits. Earlier bits stream into the context FIFO. Both roots and the residual class are ready at the delimiter. For existing contexts, prospective prefix comparisons, residual captures, exact duplicate comparisons and class clocks run in a fixed parallel batch. Only the selected candidate’s validation flags apply.

The stable-assignment proof handles overlapping contexts: contexts never change, and later indices cannot outrank a word’s first assignment. It is important not to claim injectivity of arbitrary tagged residuals. Only produced receipts have unique tags; all query lanes still have exact full-word witnesses.

An independent adversarial reviewer read the complete draft and checked capture timing, delayed receipt comparisons, zero residuals, duplicates, empty contexts, late overlapping contexts, current-version roots and query deadlines. The review approved the construction after two wording corrections: residual bits, rather than query bits, in producer comparisons; and explicit discarding of unchosen candidate flags. The independent audit imports none of the primary model.

The primary model reuses the maintained pending-substitution model for immutable committed tries, installers and pending readers. It checks the new streamed producer and readers that start after different context lengths. The independent audit compares a rolling-deque producer with a separately coded literal-set and slicing definition.

These are finite semantic checks. Host-language maps, tuples and arithmetic are not native instructions; the complete proof supplies the bounded local schedule. The two audits have different implementations and oracles. The primary deliberately shares the older pending implementation to exercise the integration dependency.

Comparison and qualifications

This is a written extension of the lab’s previous native constructions, with no new external theorem imported. Reader section 15 supplies residual-scale service and exact pending negative readout. Reader section 18’s fixed normalizer does not itself authorize an input-learned normalizer. The new work supplies a paid producer for that learned representation and prospective query starts, then carries the dependent fixed-context extension through the same assessment. No external priority or root claim admission is asserted.

Entry 129 remains an imported matching/positive-path interface bound with a growing alphabet. The new machine has no asserted homomorphic matching-diagram summary. It recognizes a checked right-first language; its PEG consequence concerns reversal of that complete encoding. Actual literal preparation, all old observations, discarded prospective work, allocation, routing and retained versions count. No ready handles, decomposition, padding, address operations or EOF service are introduced.

The former full-name dispatcher remains a failed implementation. It is not a native-language lower bound: the new construction is a concrete escape for its common-stem witness family. Existing replay, affine joins and causal/unary scaffold results remain controls with their original contracts. Independent-store composition remains a separate problem.

Next decisive target

Replace the fixed context tuple by an input-learned hierarchy with unbounded leaves. Test late shorter contexts and long nested chains. A successful extension must bound current-version access and all pending-work disturbance while starting each required residual reader in time; merely storing a shorter code at a leaf is insufficient. After this access step, return to complete clipped-cone interval profiles, their ordinary-input completeness producer and future activation. Unrestricted radial profiles and independent-store joins stay open.

Integration disposition

Source custody: original proof and two code audits only; no primary-source PDFs, extracted text, private scratch or correspondence. Claims: written native theorem 68, no root CLAIMS.yaml change. Evidence: complete maintained proof, primary integration model and independent audit. Failure ledger: the old per-selection stem jobs remain refuted, with a proved shared-context escape and explicit fixed-context limit. Frontier: hierarchical context access above. Reader synthesis: the existing composition program and homepage entry. Site representation: generated styled proof/review and syntax-highlighted source readers with exact downloads, preserving prior routes and paper order.

Scheduled 111 to 112 and mathematical 130 to 131 are counted once for the combined producer, reuse theorem and fixed-context extension. Window three, last reassessment 128. Next scheduled 113 is research, editorial 114, primary-proof review 115. Publication and retries add no counts. Exact build, source and deployment receipts belong to the integration state.