Assessment170: dense suffixes finance short-name composition

9 October2026. Dedicated two-paper primary-proof review and one written native construction. The maintained proof is reader47 in the composition argument. The prepared compiler remains separately maintained. No new root admission.

Result and significance

For fixed r,B,C, let n0 be the first actual right-target length. Target lengths lie in [n0,2n0], right keys have length at most C*n0, and their number is at most floor(n0/4). Under46’s final slice-rank and coefficient-prefix-breadth gates, short ordinary keys now support unbounded target rows and arbitrary left fanout. There is no lower key-length bound. All symbols, discarded preparation, retained history and final pins remain charged.

The producer services one old job during the next actual target, refreshes the current key, catches up buffered target bits, and validates the current word before its delimiter. The final exact publication leaves a dense own-slice suffix. That suffix pays for the entire immutable subset-action compiler. 12.2’s suspended pointer-payload capsule then stores each left source’s state without an upward walk, even when source and intermediate lengths are unrelated.

This is an extension of known persistent representations and rebuilding ideas through the Lab’s native primitives. Confidence is high in that classification: we add a checked literal-input schedule, final-release bound and source/pin composition, rather than a general new persistence transformation. Comparable widths and bounded population remain essential to this proof. Broader priority or a characterization is not inferred.

Primary-proof review

Both complete papers were read. PDFs and extracted/OCR text remain outside the repository. The second source’s scanned equations were inspected visually on PDF pages10-11 (printed4-5), after reading its entire OCR extraction.

Demaine, Langerman and Price

Primary author edition: Confluently Persistent Tries for Efficient Version Control, 18 pages; preliminary conference version SWAT2008. SHA256 8768751ba0e092cf1e2ba27ebbb0bc73f77e86b3a7ba60e1b01079fcc896a5a6.

The model keeps constantly many fingers, constant-size node information and constant-time edge-label comparisons. Section2 compresses the Steiner tree between fingers; deques represent intervening paths. Local changes repair only constantly many finger/path structures. Section3 replaces external parent pointers by relative fingers, uses heavy paths and telescoping biased-tree depths, and repairs passive fingers. Its navigation and update bounds differ. The hashing variants in4-5 cease to be purely functional and use expected amortized bounds. Section5.1 rebuilds from pristine structures, replays recorded updates into paired replacements, and charges overflow to shortened update lists. Its capacity-blind observational-equivalence premise is explicit. Section5.4 separates keys into weight-ranked groups and bounds movement across those groups. The final open problem asks to combine the two functional bounds. These are located-subtree operations, not pointwise union or a final-symbol ordinary-name recognizer. Their primitives do not replace our paid routing, strict FIFO specialization, or last-publication argument.

Application judgment: a free finger would conceal exactly the key-replay debt that47 pays. Copying a subtree can retain a classifier but cannot retroactively install new actions in old compiled states. We therefore use the paper as an operation-contract control, not as a direct constant-overhead native reduction.

van Leeuwen and Overmars

Primary report: The Art of Dynamizing, RUU-CS-81-8, April1981,18 PDF pages including front matter,11 numbered text pages. SHA256 a62e834bd0426bc3c8e939475431d671d800b20610b06bbebbf0c3faf0783714.

Section2’s Theorem1 assumes weak updates and smooth construction/query bounds. Its proof keeps OLDMAIN usable, constructs MAIN, buffers updates, and then replays the buffer while servicing new arrivals. The construction-plus-replay calculation finishes within n0/6 updates; the old structure remains within its weak-update allowance. The theorem does not require decomposability. The subsequent equal-block proof identifies size doubling, halving and oversized blocks as rebuild triggers separated by linearly many updates. The logarithmic and general tradeoff discussion then combines block families. Sections3-4 apply the framework and delimit its role. Several optimality and application theorems are cited from other papers; their omitted proofs are not independently reconstructed here. Querying all blocks is paid, and the model is not our immutable old-top, ordinary-symbol model.

Application judgment:47 uses the same separation between construction debt and catch-up debt, but its clock is actual symbols. It does not need OLDMAIN to answer compiled-table queries during the right block, so it can abandon a stale compilation. Producer roots, however, must remain coherent while a target is replayed. The two timing obligations must not be conflated.

Quantifier and resource comparison

The imported papers do not prove these rows; the new written schedule does. The review closes the attempted direct imports and supplies the useful rebuilding/catch-up distinction. The result remains a subclass construction.

Adversarial audit and finite evidence

The writing-agent audit checked: - first-word bootstrap does not need a width header or a prebuilt ruler; - an overlong initial key is rejected by paid scanning during the first target; - a repeated key sees the previous job’s new root before duplicate detection; - target reversal completes before front consumption, including alternating bits; - exact logical certificate deltas are not re-applied during path materialization; - the compiler uses only the published classifier dictionary and coefficient root; - certification/count changes do not restart a finished semantic compiler; - unready slices cannot be silently treated as absent from its snapshot; - coefficient transactions finish before current target traversal begins; - left source closure uses12.2’s explicit-tip capsule, not O(|u|) delimiter work; - full/empty slice constants stay in terminal masks, not nonzero support; - empty input blocks, absent names, prefix names, duplicates and short rejected targets have bounded-work branches.

tools/research/check_comparable_width_release.py passed:

{
  "sequences": 1728,
  "records": 5184,
  "retained_checks": 62208,
  "stale_lookup_witnesses": 1,
  "queue_checks": 1536,
  "final_word_rejections": 7,
  "restart_checks": 2080,
  "finite_margin_checks": 225,
  "source_versions": 54,
  "compiled_horn_answers": 5184
}

The checker has immutable record tries and explicit queue phases. It compares literal membership and source snapshots with set-based oracles, including parity masks beyond radial rows. Learner/publication microsteps are represented by a bounded delay; source capsule timing and spectral learning are inherited written primitives, not freshly emulated in Python. Margin tests use declared illustrative constants, not measured native rates. No independent agent or formal replay is claimed. Repository and rendered-route outcomes are in the integration receipt.

Failure evidence and seven surfaces

The stale-before-job lookup fails even on two identical consecutive records. A candidate-cardinality check alone misses an outside last word. These exclude the corresponding schedules, not alternative native representations. Restarting on every raw/certificate event would destroy the dense final window; restart only on completed semantic publication. Reopen arbitrary-width rebuilding only with a paid repair or a new lower bound on the remaining actual suffix.

Custody: original proof/checker and primary identities only. Claims: one written native extension, no root admission. Evidence: general schedule plus scoped finite checks. Failure: the precise stale, late-validation and over-restart routes above. Frontier: semantic union complexity and unequal-width repair. Reader synthesis:47 in the maintained composition note. Site: existing program entry and research note, no new paper or significance-order change; publication from the pinned GitLab projection with receipt in integration state.

Cadence and next test

Scheduled74->75 once; dedicated review170 completed. Next76research, next review80. Mathematical113->114 once, six-result window3->4, last reassessment110 unchanged. The global dispatcher, compiler margin and source closure are one native result, not separately counted observations.

Next: replace the raw row-population bound by semantic union complexity. Give a paid compiler for a growing family with few distinct unions, including ordinary new-name actions and immutable current-version destinations. Then test unequal widths, where a final short slice can invalidate a large compiled interface without enough suffix to rebuild it. Preserve exact-rank validation, independent joins and all earlier SAT/scaffold frontiers.

Validation receipt

Both finite checkers passed, as did Python syntax, evidence links, cadence consistency and whitespace checks. Full make verify was run after restoring the declared environment:1490 passed,1 skipped,5 failed in231.33s. The failures are the same four custody-provenance checks and unavailable-lake frontier verifier; later make targets were not reached. No full-suite success is claimed. The Site build produced349 styled HTML readings with raw Markdown excluded. Six structural checks and three changed HTML routes passed, including the homepage, program page and complete composition note. Final deployment and exact source-parity receipts are recorded in docs/integration/state.json. The review is independent work on old public persistence sources, not a response to a named active preprint; no embargoed contents or correspondence were used.