Assessment 242: unbounded filler fibres and current pending answers

13 October 2026. Scheduled completion 147; research assessment. Proof, independent checker.

Mathematical result

Written construction 84 removes construction 83’s fixed occupied owner-fibre bound. The injective shared key E(w) alpha E(v) exposes the namespace-known filler before the late short key. Each source retains its full activation root, an installed reordered root and one pending owner receipt. Its next actual record pays to drain that receipt; a query compares it directly alongside the installed reader. No namespace broadcast, fibre scan or final flush is used.

The exact invariant equates each foreign owner’s full activation bit with its installed reordered bit OR exact pending equality. Induction covers interleaved sources, repeated activations, primary records and complete-triple alias rollback. Explicit release windows pay the filler during a, alpha during early z and the encoded synchronous output during late z. Common owner width, local first-foreign seeds and synchronous short programs remain hypotheses. This is not a general native lower bound or a free join of independently allocated heaps.

Independent adversarial review and reconciliation

The independent reviewer read the draft against construction 83 and section 15 of the earlier composition argument. Review approved injectivity, alias rollback, descriptor currentness, same-source installation and pending readout, with two clarifications incorporated in the maintained proof:

• Pending v must exhaust exactly, even when its length differs from the queried namespace’s ell.
• The four late key jobs have a separate fixed setup/terminal observation sub-batch. No fifth traversal is hidden inside that allowance.

The reviewer independently authored the checker. It uses set/string semantics and explicit unit-job releases, not the proposed native implementation. Fresh execution passed 1,680 injectivity cases across differing v lengths, 540 interleaved updates, 2,142 immutable snapshot checks, 132,876 semantic reads and 3,156 deadline cases. A 256-owner fibre with only the final pending owner activated verifies the no-flush example. These finite checks corroborate the written argument; they do not verify the complete preparation syntax or compile a native automaton.

The checker finds a collision for an unencoded filler key: at n=9 and alpha=111000000, (v,w)=(11,111) and (1,11101) give the same alpha w E(v). Self-delimiting E(w) avoids it. Immediate reordered insertion also lacks a justified final deadline; the exact pending overlay is the repair. Short next records would break this particular installer if the common-width condition were removed. None of these failures is an unrestricted impossibility theorem.

Contribution and controls

Section 15 already proves the usefulness of installed dictionaries plus exact pending words. Construction 83 already pays learned filler discovery, synchronous short maps and finite-fibre readout. This extension changes the shared key order and couples paid deferred updates with factored query comparisons, eliminating the finite fibre bound. It is a written extension of established Lab machinery, with no external priority claim. Imported entry-129 matching/positive-path bounds are unchanged.

Replay still charges every reader; affine joins do not grant coordinate routing; causal persistence does not grant current access for free; unary coherent consumers do not supply arbitrary branching joins. Ordinary native SAT input and PEG reversal qualifications are retained. No root CLAIMS.yaml entry is added or promoted.

Custody, publication and next decisive target

One maintained proof and one maintained checker live in GitLab. Generated styled readings and highlighted source pages, with exact raw downloads, project those sources into the existing Site. No primary PDFs, private notes or duplicate maintained code are added. Validation and exact deployment receipts belong to the integration state; publication does not advance scientific admission.

Next: remove common owner width using charged local length classes. Test whether section 15’s class-window installer and pending selection can be routed in time for this factored query. Preserve arbitrary whole-suffix permutations, arbitrary-name routing, cyclic sharing and heterogeneous service as open.

Scheduled and mathematical counts advance from 146 to 147 once; native construction 84, mathematical window one, last reassessment 146. Next scheduled 148 is research. Primary review and editorial duties both remain due at 150; last primary 240 and editorial 239 are preserved. No external primary review is due in this assessment. Installed reverse-writer retirement remains a separate unverified follow-up.