Learned fillers and bounded current-answer fibres
13 October 2026. Research assessment and six-result reassessment. Construction 83 is a written sufficient native subclass theorem. No root admission or external priority claim.
Contents
What was accomplished
The zero-filler restriction is replaced by independently learned binary filler words. A fixed parser shortens a foreign owner to its alpha prefix and self-delimiting short key. Preparation checks a fixed bound K on the number of distinct known owners at that key and assigns stable slots. Each source maintains a full activation dictionary and one shared shortened dictionary with K-bit terminals. An activation changes one slot, and exact original-target support selects the correct bit of an already completed current query.
This avoids the previous review’s per-match dispatch obligation. It does not enumerate fillers, visit namespace descriptors during activation, or incrementally build a multi-pattern matcher. All filler discovery and comparison occur while ordinary right records arrive. Every literal owner and filler bit remains charged input data. The final short-key producer emits two bits per late input bit, plus two delimiter bits on the last symbol; the four-job schedule covers that final burst.
The restriction is material: at most K distinct actual owners may share a short key. The first foreign incidence of each namespace must also be its actual seed, and its learned short maps must be prefix-consistent. This is a separate checked language, not inclusion of every construction-82 encoding.
Independent review and inherited mechanisms
The independent adversarial review examined the complete draft against constructions 81–82 and section 18’s checked finite-fibre control. It found no mathematical blocker. Reconciliation made explicit the single transactional known-store capsule for group flags and slots, the no-lookahead seed-ruler producer, and disabled exceptional workers for uninitialized primary-only namespaces.
The full-name directory distinguishes distinct owners from duplicate incidences. The normalized count assigns only finite slots. This is the established section-18 argument, now on owner names. Here the normalizer also uses the input-learned alpha boundary; the result is not merely an invocation of section 18’s fixed whole-name subsequential transducer. Its normalized right-degree and length-comparability hypotheses are not imported. The present proof instead builds learned filler descriptors and pays current owner lookup with the actual remaining query symbols.
The two-root mask form completes the dependent fixed-K extension of the injective K=1 case in the same result. No separate result is counted for that extension. Provisional work, coherent old versions, exact support, negative output and the native reversal restriction all remain explicit.
Independent finite evidence
The readable checker was written independently of the proof author and rerun after reconciliation. Seed 241 gives:
| Check | Count |
|---|---|
| Parser cases against a decomposition oracle | 1,023 |
| Registry and duplicate-reuse checks | 72 |
| Expected rejections | 42 |
| Current-answer comparisons | 131,880 |
| Retained-version checks | 672 |
| Four-job release schedules | 2,112 |
| False-positive control when slots are omitted | 1 |
The comparisons include mixed short-key lengths, arbitrary fillers, synchronous noninjective maps, ordinary and exceptional support, missing targets, aliases and separate sources. Python containers are semantic oracles, not a native implementation; the job queue corroborates the written release schedule rather than measuring native time. The exact ordinary grammar, local producer and compiler transfer rest on the written argument and their stated inherited primitives.
Six-result reassessment at mathematical 146
The six results since reassessment 140 have a coherent two-part structure.
| Construction | Structural progress | Remaining restriction |
|---|---|---|
| 78 | A meaningful suffix pays learned prefix reindexing | The suffix is unchanged |
| 79 | Learned suffix programs with paid bounded delay | Fixed delay bound |
| 80 | Growing delay and bounded speculative branches | Checked release envelope and bounded simultaneous width |
| 81 | Earlier shared activation indexes bypass long private paths | Common contraction shape |
| 82 | Universal boundary charts handle different lengths and positions | Zero filler and specified seed contracts |
| 83 | Checked owner-fibre masks handle learned filler contents | Fixed occupied fibre capacity and timely short-key programs |
The first three pay for producing and servicing query work. The last three change the maintained coordinates so that less work remains at query time. Together they support a useful sufficient criterion: current answers compose through a shared representation when ordinary input pays its updates and a locally available query program reaches the selected current predicate before the deadline. A semantic quotient or a total-work estimate supplies neither obligation alone.
The intervening service-game, cross-index and matcher failures remain valid for their specified implementations. They explain why a change of representation was needed; they are not universal barriers. The strongest surviving obstruction is not merely too many stored answers. Independent activation bits inside one normalized fibre remain distinguishable, and the question is how their selectors and current values can be locally accessed on time.
Contribution assessment: the six constructions are written extensions and combinations of the Lab’s established dictionaries, queues, finite lanes and native compilation controls. The present advance is the charged composition of checked owner fibres, learned fillers and short-key readout. It does not settle the natural SAT/scaffold boundary, characterize every reusable dependency pattern or establish an unrestricted native lower bound. Root claims, imported entry-129 theorems, replay slices, affine joins, persistent causal algebra and unary coherent cubical algebra retain their own hypotheses. No free join of externally prepared heaps or feedback closure follows.
Failure boundary and next decisive test
A Boolean shortened-key entry merges two independent owners and gives a false positive when only one is activated. Fixed slots repair that case; a K+1st distinct owner at the same key is rejected by this construction. Increasing K with the input would break the finite-label contract and is not an extension of the theorem.
Next: allow unbounded occupied owner fibres through a checked shared inner representation. Charge the construction of its selector route and the current-answer update. A selector arriving at the final symbol may select a completed answer but cannot initiate an unbounded traversal. Seek a useful subclass with no per-namespace updates or final replay. Arbitrary whole-suffix permutations, arbitrary-name routing, cyclic sharing and heterogeneous service remain open.
Scheduled 145 to 146 and mathematical 145 to 146 count once for this completed result. Native construction 83; six-result window resets to zero, last reassessment 146. Last primary review 240 and editorial 239 are preserved. Next scheduled 147 is research; scheduled 150 requires both primary review and editorial work. Publication receipts and verification limits are recorded with the integration state rather than changing their own source projection.