Assessment 180: completion debt and the release of correction work
9 October 2026. Dedicated primary-proof review 85. This is a sustained unsuccessful transfer attempt with a sharper operational test. There is no new native recognition theorem or mathematical-result increment.
Contents
Outcome
A restart-free snapshot compiler plus a linear-size update log does not yet meet the final-symbol deadline. The remaining input can pay for the compilation while failing to pay for a correction released only at its last symbol. The maintained argument, section 7 gives the exact workload identity, a sufficient bounded-arrival contract and a literal accepted final-two-profile family defeating whole-record replay. The Python checker retains the previous completion tests and checks these new finite diagnostics.
This comparison revisits mechanisms previously studied in assessments 159 and 164. Their novelty status has not changed. The new question is whether completion debt can replace the queue’s front reserve and make a persistent correction worker finish at every valid terminal boundary.
Primary arguments studied
Hood and Melville: readable copying in pure LISP
Robert Hood and Robert Melville, Real Time Queue Operations in Pure LISP, Cornell TR80-433, July 1980. Primary report, repository record. SHA256 f2e94253671f72484ce3798ab631fadefb3bb784ed030079097132303ffb15a9.
The full report, including its recopy invariant and implementation appendix, was re-read using OCR and page images. The two-list amortized argument first identifies reversal as deferred work. The real-time construction starts before the old front is exhausted, reverses and assembles incrementally, and services copying during updates. New insertions enter a separate rear; deletions alter the live front and copy bookkeeping. The old front remains directly readable. The reserve proof bounds copying by the number of operations possible before that front disappears. The appendix uses a fixed record and unary unit arithmetic.
Our transfer test separates storing an update from executing it. The queue receives a ready item handle. Its theorem does not include discovering a named row’s current class or executing an arbitrary operation encoded by that item. The positive mechanism is immediate absorption of updates into a semantically readable incomplete representation.
Driscoll, Sarnak, Sleator and Tarjan: structural persistence
James R. Driscoll, Neil Sarnak, Daniel D. Sleator and Robert E. Tarjan, Making Data Structures Persistent, JCSS 38(1), 86–124, February 1989. Author PDF, DOI 10.1016/0022-0000(89)90034-2. SHA256 71f7770e1b0ecc76fe76fe99ec0d15e5da25dc27b1cee9299a70375c8b567a68.
The complete selected argument is partial-persistence node copying: sections 2.3.1–2.3.4, including representation, update, predecessor repair and potential cancellation. Section 1’s model, section 2.2’s fat-node alternative, sections 3.1–3.3.3’s version navigation and section 6’s qualifications were also compared. This is not a fresh review of all balanced-tree proofs.
Bounded extra fields postpone copying; overflow creates a new node and propagates pointer changes through boundedly many predecessors per copied node. The potential pays cascading copies in aggregate. The operational correspondence is restored before the next public operation; versions use supplied access pointers and version selection. Bounded in-degree is essential to this analysis. The write-once/pure-LISP consequence is a linear-time simulation, not the fixed per-symbol old-top implementation requested here.
Our histogram has arbitrarily many row aliases to shared bucket metadata. Both the alias bound and the timing contract therefore require a new implementation before importing this copying theorem.
Exact contract comparison
| Obligation | Queue proof | Node-copying proof | Completion-debt attempt |
|---|---|---|---|
| Input object | Queue operation with ready item | Access/update steps on a linked structure | Ordinary characters; fresh-pair status learned during parsing |
| Initialization | Empty fixed queue | Empty structure and named access pointers | Fixed native state; no prepared class list |
| Dependency control | Front/rear lists and copy counter | Bounded live predecessor count | Unbounded aliases and changing gaps |
| Cost guarantee | Worst-case bounded operations | Amortized update overhead; bounded access overhead | Fixed service per actual input symbol |
| What remains readable | Current queue front | Completed public versions | Current class interpretation must still be supplied |
| Work horizon | Front cannot empty too soon | Aggregate potential over updates | Mandatory future coalescence, measured in encoded symbols |
| Missing reduction | Queue item is not an executable correction | Pending cascade is not a native current-version reader | Streamed correction, release bounds and final selection |
No growing alphabet or finite-state diagram bound is substituted for these native resources. Old-storage observations, initialization, allocation, name and pointer routing, update capture, retained log storage, compiler steps and output all belong to the charged contract. A pointer-machine primitive or integer version comparison is not a finite-label instruction without implementation. Negative tests must use allowed local observations, with no identity, address, metadata, timing or control-flow channel.
Dependent attempt and useful failure
Three stages were tested. Freezing a snapshot preserves its old interpretation and avoids repeated restart work, but it does not answer current queries. Capturing updates in a real-time queue avoids expensive list concatenation, but replay still has a release time. Finally, charging total replay length to total later input fails on the last record: a protocol that waits for certification before traversing its saved target has unbounded residual work at the delimiter.
The witness uses two completed radial rows and a third missing exactly one target of width L. That target completes the third row into an existing profile. The final relation has exactly two profiles, the preceding weighted completion debt is 11, and the final literal has L+10 symbols. A fresh L-step replay released at its final symbol misses any fixed allowance for sufficiently large L. The restriction concerns that replay protocol, not all classifiers; streaming capture, maintained cursors and readable shared corrections are explicit escape mechanisms.
The exact single-server workload identity explains the failure through suffix demand, independently of the earlier amount of idle service. A sufficient replacement requires bounded work release per symbol, enough initial completion reserve, and a pending-state interpretation respected by every update. This is a conditional interface, not its implementation. The current attack therefore ends at an operation-level bottleneck rather than claiming that the literature solves the alias problem.
Evidence, custody and next target
The checker passed 20,460 workload cases against an explicit unit-work queue, 3,450 bounded-arrival cases and nine literal radial terminal witnesses. It also reran the existing weighted search, debt-drain and late-restart tests unchanged. These are semantic experiments, not a native execution trace. General statements have written arguments. No primary PDF, OCR or page image enters the repository.
NEXT: Implement one frozen epoch’s streamed class correction: route ordinary names while they arrive, prepare the fresh/duplicate alternatives, and commit Enter/Leave plus neighboring-gap changes with fixed residual work after certification. Prove a pending-state interpretation and account for work released at each event. Test the short mover with many untouched aliases and the last long target. Only then compose epochs and spend a shared completion reserve. Final-only K=2 remains the alternative.
Seven surfaces: the maintained argument and checker are authoritative; root CLAIMS.yaml is unchanged; the release-time failure and its escape gate are explicit; the current research checkpoint, program and agenda retain the precise next test; no new paper, homepage date or claim admission is justified. Source custody remains GitLab-first. This review is a repository checkpoint; Site publication is deferred and the previously verified version 565 is retained. No new deployment or source-parity receipt is claimed.
ACCOUNTING: Scheduled 84 to 85 once; dedicated two-paper review complete. Next 86 research, next dedicated review 90, next editorial 90, which combines both duties. Mathematical 116, window 0 and last reassessment 116 unchanged. The installed legacy writer retirement remains separate, unverified and nonblocking.