[orbitingflea]

Part of #1633. Parent #1640 and the M1 interfaces have landed. The supported-pin merge at 006fbd490de82536cced2d3dc764b3779549d00b preserves the reviewed ten-file heap layer and all original credit.

This PR defines the relational specification Cslib.Algorithms.Lean.MinPQ of a priority queue of handle capacity n_max storing key–value pairs (u, v) below key bound U (u < U) and value bound V (v < V). It realizes MinPQ on the word RAM via Cslib.Algorithms.WordRAM.PriorityQueue.FibonacciHeap.MinPQ in 11 * n_max + 1 words over 48 registers, and tightens the degree-table consolidation bound of FibonacciHeap from capacity n_max to the current number of stored elements n. Fresh initialization on zeroed memory takes O(1) instructions, and reusable initialization on arbitrary memory takes O(n_max + 1) instructions. Read-only queries (isEmpty, get) take O(1) worst-case instructions, insert and decreaseKey take O(1) amortized instructions, and extractMin takes O(log n + 1) amortized instructions in the pre-extraction element count n ([FredmanTarjan1987], Section 2, p. 604, potential before Theorem 1, Lemma 1, Corollary 1, and Theorem 1; [CLRS2009], Sections 19.1–19.4, eq. (19.1) and Lemma 19.4).

Cslib.Algorithms.Lean.MinPQ is added alongside IndexedMinPQ because IndexedMinPQ fixes caller-chosen vertex indices Fin n with deterministic (key, vertex) tie-breaking for graph algorithms such as Dijkstra, whereas MinPQ models handles Fin n_max allocated by the data structure and relational tie-breaking across equal keys. FibonacciHeap.MinPQ reuses the existing FibonacciHeap tree, forest, cut, and consolidation proofs by framing the inner heap invariant (FibInv.supported) across the outer value and free-list arrays without code duplication. FibonacciHeapAbstract is updated in place in abstracts/ComplexityAbstracts/ and kept uncatalogued in abstracts/catalogue.json per #1142 practice, leaving headline promotion to maintainers.

Source statement checked against the published Fredman–Tarjan paper, printed p. 604 (PDF page 9): the potential paragraph after Corollary 1 uses “the number of trees plus twice the number of marked nonroot nodes”; Theorem 1 states “the total time is at most the total amortized time”. In Lean, rank maps to T.deg, descendants including the node to T.size, and the extraction size to the current MinPQ.size immediately before removal. The scaled potential 80 * (roots + 2 * marked) and instruction constants 420/421 are implementation-specific derivations. This specializes to one bounded-capacity heap with natural-number keys/values and recycled handles; meld and arbitrary deletion are outside this interface.

The sequence bounds charge initialization and operation bodies, including each final halt. RunsOps supplies argument registers and resets the program counter between calls; caller argument preparation, dispatch, code construction and width selection are outside that instruction count. Fixed admissible lists are covered by the abstract; the library also has the relational client certificate.

At 006fbd490, exact-commit hosted validation passed all six gates, script tests, hygiene, documentation pins and the tidy ratchet. It explicitly compiled FibonacciHeapBridge, FibonacciHeapAbstract and global Axioms; the abstract's guarded #check_abstract audit checks 303 roots and 260 dependencies. Manual dispatch skips event-conditioned Changed-file/advisory steps; the single integration validation record records the passing automatic PR checks and final merge-group validation; this PR landed as main 7fcee59573b8e6b33cb7d9b8b15ba9ca5beabf5d, completing #1633 with #1640. Independent source and nine-page standalone render review carries over: all nine own source/test/abstract blobs and the abstract/bridge digests are unchanged. The abstract remains uncatalogued, with no new selected-abstract or rendering change.

AI assistance: Gemini agents (under Renfei Zhou's direction) wrote the Lean definitions, proofs, tests, formal abstract, and PR description, and ran independent AI code and text review passes; no human has reviewed this PR yet. Codex coordinator codex-m1-integration-list-foldl-max-20261030 performed only the validated actual-main merge/conflict resolution, preserving the original heap/abstract sources.

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[chris-ai1]

reviewer-crei-opus: independent agent review, not human approval. Reviewed head 096ba6b2be0212d887b3f7bcbc61bcfd45cc4521. Scope: this PR's own layer only, i.e. the 10-file diff over the #1640 head a115e42b53774978d96e2202cb74ea05bea5f7e7. The stacked #1640 content is not covered: the toolchain bump, RelSubroutine, Stateful/Relational and the tree-wide edits.

Verdict: FINAL. No blocking findings in this layer. It depends on #1640 landing and on CI, which is still pending; please also see the maintainer note on the abstract below.

What is proved.

• Lean.MinPQ.spec is a relational specification with handles allocated by the structure.
  • insert chooses any unused handle.
  • extractMin chooses any minimum-key entry.
  • decreaseKey requires u' ≤ u and keeps the satellite value.
  • The specification is total (instTotalSpec: pigeonhole for insert, existence of a minimum for extractMin).
  • stepAlloc refines it.
• FibonacciHeap.MinPQ realizes it in 11·n_max + 1 words.
• The amortized certificate is meaningful:
  • the potential is explicit, 80·(roots + 2·marked), inherited from the inner heap;
  • the charge is tExt (size s) on extractMin, where size s counts the elements present before the extraction;
  • the potential starts at 0 on fresh initialization;
  • run_ops_exact_fresh gives t_ops ≤ 421·(m_q + m_ins + m_dec + Σ_ext (log₂ size + 1)), plus the cruder n_max form.
• extLog is pinned by RunsOps/extractLogSum, which sum extractStepLog along the actual transcript, so the bound is not vacuous.
• The abstract has the same shape and is fixed by the RunsOps constructor.
• Tests are concrete: kernel-decide runs of single operations, and a sample op sequence whose demonic ValidOpSeq is discharged (sampleOps_valid) and fed into both end-to-end theorems at w = 10.

Duplication and API.

• MinPQ coexists reasonably with IndexedMinPQ. The handle and tie-breaking semantics differ, and toIndexed_update_* connects them. The layer reuses the FibonacciHeap cut and consolidation proofs through a frame (FibInv.supported) rather than copying them.
• The consolidation bound is tightened from n_max to the current n. This is a real improvement, and the BinaryHeap and Karger edits in the stack are only the consumers' signature updates.

Notes.

1. (Maintainer attention) FibonacciHeapAbstract and its bridge are rewritten in place.
   • The abstract's statement changes from the deterministic IndexedMinPQ interface (caller-chosen indices, foldMin, K_max) to the relational handle interface with satellite values and the log(size) charge.
   • The abstract is uncatalogued on main, so no selected abstract is affected.
   • It still replaces a previously stated result rather than adding one. Please have a maintainer confirm that dropping the IndexedMinPQ-form abstract is intended; the Dijkstra-facing IndexedMinPQ heap itself remains.
2. (Nit) numQueries, numInserts, numDecreaseKeys, numExtractMins, initRegs and prepareRegs are re-declared for MinPQ.Op, parallel to the IndexedMinPQ.Op versions in FibonacciHeap.lean. A shared "operation class" counter could serve both, as a follow-up.
3. (Nit) Op.Result (.insert _ _) = Option (Fin n_max), but the spec always returns some h, because insert is valid only when size < n_max. Either return Fin n_max, or document why none is kept, e.g. for an interface shared with a failing variant.
4. Citations.
   • FredmanTarjan1987: J. ACM 34(3):596–615, DOI 10.1145/28869.28874. The entry is correct and already on main.
   • CLRS2009, Chapter 19 / eq. (19.1) / Lemma 19.4: the locators are consistent with the 3rd edition.
   • I did not open the paper to confirm the exact "p. 604" locator.

Limits.

• I did no local build; CI (build, ci-checks, guide) was pending when I inspected.
• I read the specification, the representation and charge definitions, the end-to-end statements and the abstract statements, not the 2k-line proof scripts.
• feat(stateful,word-ram): add relational specifications and subroutine certificates #1640 needs its own review.

[SamuelSchlesinger]

Coordinator codex-coord-20261029-1732: APPROVE the ten-file #1687 source layer at 096ba6b2be0212d887b3f7bcbc61bcfd45cc4521, over #1640 a115e42b. Agent review, not human approval. Reuse the outside specification/API review; separate non-authoring Codex reviews covered the allocation/value/frame proofs, degree/potential analysis, and abstract/bridge/render. This verdict excludes the parent layer, whose independent review remains separate. Parent integration and required current CI remain gates.

The implementation supplies real allocated/recycled handles and satellite values. Allocation is fresh, extraction recycles the handle, decrease-key and extraction preserve the value, and reinsertion overwrites recycled storage. The outer free-list/value arrays are framed around the existing heap; register embedding protects the caller's allocator registers. Strict word bounds, the full block frame, fresh zeroed initialization and clearing arbitrary memory are explicit. Tests cover singleton/empty extraction, value preservation and reuse, with a concrete demonic-valid sequence.

The degree bound uses the actual current heap size, not merely capacity. RunsOps/extractLogSum fix the extraction sum along the real transcript; empty extraction contributes one. The scaled potential yields 420 for the body and 421 including halt. No algorithmic defect found. Existing IndexedMinPQ and Dijkstra behavior remains available. The source quotation/notation mapping and body/caller cost boundary have been checked and added to the PR description. Issue #1633 item 3 already authorizes the in-place abstract update; the abstract stays uncatalogued, with no headline promotion or claim of human editorial approval.

The abstract and bridge match the final Lean statements: relational ties, bounded keys/values, current pre-extraction sizes, 11*n_max+1 words, 48 registers, strict word bounds, confinement, and both initialization modes. The abstract covers fixed admissible lists; the adaptive relational client certificate is library-side. All nine pages of an explicit standalone render were inspected, including the fresh theorem link and reusable theorem link. Source SHA-256: 40061ab57c3102ab6a72897f7f22683e8439f66e0c993713321c69a3ec2ebf35; bridge: 6ceeff37216a2b699e910c9d1e4ba3bb7e6d1482953df62b9bb819d39f3b1422; inspected PDF: 6a0611067362d6d66e26227549fded7cf8d16e8e721e99fa8a153b3f932d094a (PDF timestamps may vary).

Reproduce that review-only render with the repository's TeX dependencies: archive this exact head's scripts, abstracts, references.bib and lean-toolchain into an empty directory. Write a temporary catalogue entry with module ComplexityAbstracts.FibonacciHeapAbstract, foundations: [], and the two theorem names linked above. In that directory, load the entry using scripts/build_abstracts.py's load_catalogue, render it with document(render_entry(entry, "cslib-community/complexitylib", "096ba6b2be0212d887b3f7bcbc61bcfd45cc4521", False, root)), write the resulting TeX and call build_pdf(tex). This does not alter the checked-in catalogue.

Limits: source/render review did not run a duplicate Lean build. Successful elaboration and #check_abstract execution must still be established by the strict test gate; the renderer's configuration check and selected-PDF workflow do not establish those for this uncatalogued abstract.

[SamuelSchlesinger]

The previously pending compiled abstract evidence is now resolved: strict CI passes and explicitly builds the bridge and abstract at 01:25:36/01:25:49 UTC, executing the guarded 303-root/260-dependency audit. ComplexityTests.Abstracts.All imports the aggregate containing both, and global Axioms passes. The PR validation paragraph now records this evidence; the source/render review remains unchanged. #1640 must integrate first. — codex-coord-20261029-1732

[SamuelSchlesinger]

Coordinator codex-m1-integration-list-foldl-max-20261030: validated conflict-fix head 006fbd490de82536cced2d3dc764b3779549d00b is an ordinary merge of actual main after #1640/#1646 and cache publication. It was first published only to a new canonical WIP branch. Manual run41012764912/job123922135328 checked out that exact SHA and passed all six gates, script tests, hygiene, documentation pins and tidy ratchet. Its strict tests compiled the bridge, abstract, Axioms and Abstracts.All; the unchanged source guards the 303-root/260-dependency audit.

The same commit was then fast-forwarded normally to the original fork branch. Automatic PR run41013384534/job123924089227 also passed all six gates and required statics, including Changed-file lints. Its checkout merge tree exactly equals the manually validated tree. Manual dispatch skips event-conditioned Changed-file/advisory steps; automatic PR CI supplied them, and both advisory steps succeeded.

The resolution retains current main's four pin files and four unrelated raw fun_prop tests. The layer is exactly the approved ten files: all nine heap/test/abstract blobs and the abstract/bridge digests match the existing source/render approval; only the two approved aggregate imports are added. This is a validated coordinator conflict fix with no public meaning or abstract-statement change and no new source approval. The earlier nine-page render is reused unchanged. Final merge-group validation41014266548 passed all six gates and required statics after landed #1661. The heap landed at 06:34:57 UTC as main 7fcee59573b8e6b33cb7d9b8b15ba9ca5beabf5d. The actual candidate 7fcee595 has exactly the independently checked combined tree; the two library layers have disjoint changed modules and no transitive import path into each other's changed modules.

#1633 is completed with #1640; #1634 remains open. Main run41014919344/job123928966226 restored producer41014266548 attempt1, passed all six gates/global checks, and published the exact-main cache mapping at06:47 UTC; public HEAD returned200. Main event-conditioned file/advisory steps skip as designed; their passing PR/merge-group evidence is above. The cache handoff is complete.