Assessment 243: shared current answers across length classes

13 October 2026. Scheduled completion 148. Written construction 85 and independent checker.

Result and exact scope

Construction 85 removes construction 84’s global owner-width condition. Each source has a full activation trie and a paid class directory with one installed shared trie and one pending receipt per class. Actual owner bits service the current/next window before a pending replacement. A final query selects its class during its namespace spelling, then pays both installed-key access and pending parsing during later ordinary fields. No distant pending scan, per-namespace update or final flush is required.

All owner widths are odd and at least 17; each incidence checks matching owner/namespace width. Namespace-local seeds, contraction inequality and synchronous short maps remain required. Unbounded fibre sizes and arbitrarily interleaved length classes are admitted by one fixed machine. PEG recognition is only for reversal of the complete checked language. No general native lower bound or new root admission follows.

Independent review and finite evidence

Independent adversarial review compared the construction against construction 84 and section 15’s class-window pending overlay. It approved the invariant, per-row width bootstrap, shared key injectivity, directory service and query release windows. Reconciled details are explicit in the proof: jobs are bounded macros; completed earlier drains remain provisional, unpromoted future work is discarded, alias 1 restores the full header; ill-shaped final targets disable unsupported candidates rather than reject otherwise valid SAT syntax.

The independently authored checker passed fresh execution: 223 known owners across nine widths, 360 interleaved updates, 1,077 retained-snapshot checks, 51,696 semantic reads, 11 installation-window budgets, 32,131 query deadline cases and 1,880 injectivity cases. A selected pending owner of another width in the same class correctly fails the query’s width test. These are finite set/string semantics and normalized service tests, not a compiled native implementation or full preparation-syntax verifier.

Contribution, failures and controls

Section 15 already provides local length-class windows and exact pending overlays. Construction 84 already provides early learned-filler routing and factored pending comparisons. The extension proves that these operations fit together: a width-tagged shared key prevents cross-width ambiguity, namespace input pays bucket selection, and the subsequent query fields pay parsing even a larger pending receipt in the same class. This is a written extension of those methods, with no external priority claim.

A global pending slot cannot safely replace an unfinished long receipt on a short update; a global pending list lacks the bounded parallel-comparison argument. Class-local pending storage repairs these specific routes. The local owner/namespace width relation remains load-bearing for this proof. A much shorter query selecting a much longer owner is not covered.

Replay, affine joins, persistent causal algebra and unary coherent consumers preserve their earlier scopes: sharing is not free routing, merging or current observation. Imported entry 129 state/port bounds retain their exact interface hypotheses and growing alphabet. Root CLAIMS.yaml and all prior results remain unchanged.

Custody and continuation

GitLab maintains the proof, checker and this review. Generated styled HTML/KaTeX and highlighted source with exact downloads project these maintained sources into the existing Site. No private scratch or primary PDFs enter public source. Scoped rendering and publication receipts are recorded in integration state; publishing does not promote scientific admission.

Next: test cross-scale reuse where a much shorter ordinary target selects a much longer activated owner, with unbounded image and no supplied route. Determine whether paid preparation can supply a shared current predicate without a long query-time traversal. Section 15’s explicit-installer obstruction is a control, not a universal lower bound. Preserve arbitrary whole-suffix permutations, arbitrary-name routing, cyclic sharing and heterogeneous service as open.

Scheduled 148 and mathematical 148 complete once; native construction 85, mathematical window 2, last reassessment 146. Next 149 is research. Both primary review and editorial duties remain due 150, with last primary 240 and editorial 239. Installed reverse-writer retirement remains separate and unverified.