Assessment 208: early routing and the learned-hierarchy boundary

12 October 2026. Research assessment; closure specialization and failed extension. No new numbered theorem, mathematical-result count, root admission or priority claim.

Result and payoff

Early unique shared routing permits unboundedly many resident theorem 68 kernels with only one active group. This checked subclass replaces a global fixed-context bound by a local one; late shorter and overlapping learned contexts still lack a charged current-union reader.

The complete argument pins the actual binary route syntax, producer, current source-group lookup, suspension invariant, negative readout and all-symbol accounting. The independent semantic audit checks retained versions and the wrapper’s two counterexamples. The inherited theorem 68 is unchanged.

A route is learned from existing ordinary names, but matching selection/target routes are a checked admission restriction. This is not a reduction that inserts free headers. Fixed dictionary-interface nesting and exact committed-plus-pending state permit inactive groups to remain suspended. Prefix-free routes make ignoring all other groups sound for negative answers.

Sustained failed extension

Allowing cross-group aliases already breaks the one-group semantics: a selection stored under one group is invisible to a query routed to another. Overlapping contexts can make unboundedly many kernels relevant to one query. A late shorter parent can be linked cheaply, but neither that root link nor a trie supplies the joint selected predicate. Eager migration has unbounded disturbance; lazy linking defers the missing union readout and changes the residual-start budget. These are failures of the attempted wrapper, not native lower bounds. The full argument records exact reopen conditions.

Independent adversarial review required complete route comparison and syntax validation, current roots, fixed interface nesting and suspendable exactness. The finite audit is independent of the inherited producer implementation and does not certify native timing. Full repository verification and scoped reader checks are recorded in integration state.

Entry 129 remains an imported conditional matching/positive-path bound over a growing alphabet. No matching summary or unrestricted native lower bound follows. This construction is serial reuse, not an independent-store join; recognition transfers to a PEG for reversal of the checked encoding. Replay slices, affine joins, persistent causal and unary coherent cubical results retain their original contracts.

Disposition and continuation

Source custody: maintained original note and checker in GitLab. Claims: local closure specialization, native theorem 68 and root ledger unchanged. Evidence: written proof, independent review and finite semantic audit. Failure ledger: three explicit failed extensions in the note. Frontier: paid late-shorter-context union. Reader synthesis: this review. Site: generated styled note and syntax-highlighted source projection prepared; publication was deferred at this assessment and is included in editorial pass 209. This remains a boundary refinement with no correction to theorem 68 or new numbered result. The existing homepage research date remains unchanged.

Next: Construct or refute the charged late-shorter-context union interface: retain old child kernels without eager migration, then answer the next ordinary-name query from the current source version with bounded active readers and no lost residual-start budget. First isolate nested chains with arbitrary short aliases and selected-state collisions. Use the routed subclass as a positive control; clipped-cone intervals and independent-store joins remain separate.

Accounting: scheduled 112 to 113 once. Mathematical 131, window three, reassessment 128 and native theorem 68 unchanged. Next scheduled 114 is editorial, followed by primary-proof review 115. Preserve this mathematical target during editorial work.