Assessment 176: current count classes need version-aware routing

9 October 2026. Research assessment. The maintained argument records the complete contracts and proofs; tools/research/check_count_class_access.py is its finite corroboration.

Outcome

The current-bucket service is strictly stronger than a fixed finite pending-action mechanism. Ordinary unit increments of other rows make h untouched row handles expose h independently varying neighbor-gap bits. Exact accumulated actions have a 2^h-class Boolean deletion quotient. Applying the Lab’s existing identity-blind stable-handle theorem gives Omega(log(h+2)) worst-case cold correction time. Therefore a protocol that finishes ordinary row lookup and only then starts a constant-cost current-bucket repair cannot implement this service.

This is a written interface reduction and failed-route conclusion, not a new general native lower bound. The proof uses finite tags, fixed degree/root count, immutable old storage and identity-blind observation. Adaptive negative tests and query allocation are included. Physical identity, addresses, mutable tables, query-specific advice, storage-size, timing and control-flow channels are excluded. The supplied cold handles belong only to the stronger internal contract, not the actual native input.

The explicit witnesses have equal encoded lengths and use a fixed ordinary clause alphabet. All of them share a completion to exactly one final radial profile. This prevents dismissing the intermediate states by the final-K promise, but does not turn intermediate gap observations into the language’s final acceptance bit. The known K=1 recognizer avoids this stronger service.

Dependent attack

A full binary-count dictionary walk after each distinct-pair decision also fails its proposed deadline schedule. For a one-bit row with count at least 2^L, the next q previously absent short targets can have total spelling O(q log q), while the protocol releases Omega(q L) work. For any fixed service rate, L can exceed the available suffix budget. Earlier long target input is before release of these particular walks. This rules out that eager walk protocol, not preparation, maintained fingers, speculation or readable pending work.

The strongest surviving candidate fuses ordinary-name routing with current-version interpretation. The witness names have Theta(log h) bits, enough to pay the cold-access lower bound if those bits are used effectively. The finite persistent bit-trie control demonstrates this access distinction; its recursive path-copy updates are not asserted to meet native per-symbol deadlines.

The next test is a name-weighted proxy route with an exact pending unit move. It must handle a short row leaving many populated buckets, disappearing singleton buckets, duplicate targets and immediate short repeated names. A fixed owner slot or an unbounded uncharged epoch chain is insufficient. Construction, routing, observation, retained snapshots, allocation and final selection all remain charged.

Actual-draft audit and controls

The writer rechecked the proof against the stable-handle argument rather than claiming an independent reviewer. The h probes have counts 4i, and movers have 4i+1 or 4i+2; spacing by four prevents cross-coordinate interference. The complete-level continuation has the same target universe in every state and costs ordinary input. Equal-length suffixes prevent timing/encoded-length signals. The quotient proof does not assume physical summaries commute. The logarithmic theorem does not incorrectly require arbitrary repeated Set operations: all Boolean vectors from one prepared base suffice.

The routing separation is essential. A version-aware cursor produced during the name read breaks the cold-acquisition premise and is an explicit escape. The numeric traversal argument assumes newly released full walks; precomputed or shared routes are outside it. These qualifications prevent promotion to unrestricted native nonrecognition, SAT separation or a PEG consequence.

Fixed-bank augmented counters, bounded-live metric class repair, final-one-profile rectangle validation, input-funded compilation and earlier replay/causal/cubical controls retain their hypotheses. Entry129’s imported full-relation and port results are unchanged. No root claim changes or major-result count follow.

Evidence and seven-surface disposition

The finite checker passed 510 relation states, 3,586 gap observations and equal-length record checks, 510 common radial completions, 1,798 duplicate/reordered update words, 256 retained trie versions with 8,192 queries, and 36 exact deadline-budget examples. These are semantic checks and numerical corroboration, not native timing measurements. The prior mutable histogram checker remains the positive control.

Custody: original argument and checker remain in GitLab. Claims: supporting interface reduction and two scoped failures, no CLAIMS.yaml admission. Evidence: written proofs plus finite checks. Failure ledger: exact exclusions and reopen gates recorded. Frontier: fused current-version routing or a service-free certificate, final-only K=2 unchanged. Reader synthesis: existing program/agenda plus a styled reading and source-reader projection. Publication: source/version/parity receipt belongs to docs/integration/state.json, not an assumption from a successful build.

NEXT: Construct a name-weighted, current-version proxy route driven during ordinary row-name input, with directly readable pending unit moves. Test a short row leaving populated buckets, bucket deletion/merge and the very next short record. If that fails, isolate the exact route debt; do not repeat finite-action compression or eager binary-count walks as solutions.

ACCOUNTING: Scheduled 80->81 once. Next 82 research; editorial 84 and dedicated literature review 85. Last dedicated 175 retained. Mathematical 116, window 0 and last reassessment 116 unchanged. This completes a sustained unsuccessful attack with a sharper interface boundary; no new major result or root admission.