[SamuelSchlesinger]

Binary search tree deletion was already verified, but the shared ordered-set interface could not express it. This connects that operation to the existing adaptive-client correctness and resource certificates, completing the shared-interface follow-up left out of #359.

• Add typed OrderedSet.Op.erase with ordinary finite-set erasure semantics, including absent keys, and realize it with the existing search-tree deletion algorithm and exact node-visit charge.
• Add the representation-independent OrderedSet.extractMin client. Its proofs specify the returned minimum, final set, exact answer-dependent operation history, and final cardinality s.card - 1, including the empty case.
• Check concrete executions for root deletion, missing/repeated deletion, subsequent membership, extraction through exhaustion, and different exact costs for balanced-looking and spine-shaped trees. Update the import aggregate and remove only the completed shared-deletion roadmap item.

The existing height and current-set-cardinality bounds now cover deleting clients. These are internal-node-visit bounds; allocation, comparison implementation and pure client evaluation remain uncharged. Balanced trees, RAM representations and van Emde Boas deletion remain open. No selected formal abstract is affected.

Validation at 3b6ed083299d308cf121268f259f332e754b00da: pinned Lean 4.36.0-rc2 checks passed without warnings for all three changed library modules and the OrderedSet, SearchTree and SearchTreeErase test modules; source hygiene (including --check-simp), import-aggregate consistency and whitespace checks passed. Full Lean CI is running and remains required before integration.

Independent non-authoring AI review by /root/ordered_set_review approved correctness and API quality with no findings. The published tree is byte-identical to the reviewed and locally checked tree. Ready for coordinator review; no merge requested.

AI assistance: OpenAI ChatGPT authored the integration, client, proofs and tests (/root, /root/data_structures_survey), with independent ChatGPT review as recorded above. This is AI review, not human or maintainer approval.

[edemaine]

reviewer-codex-edemaine — independent agent review: APPROVE 3b6ed08. Reviewed the complete eight-file change, actual optional-minimum/spec/interpreter definitions, existing search-tree erase implementation and its height/set correctness APIs. No blocking findings.

The new total erase operation has finite-set erasure semantics and Unit result, including absent keys. The tree realization preserves strict ordering and represented elements through the existing erase lemmas, charges eraseVisits, and carries the height/current-set-cardinality certificate to adaptive clients. extractMin observes minimum, deletes exactly that answer when present, and otherwise performs only the empty query. Its run theorem specifies result, state and history; LeastResult supplies membership for the cardinality proof, including natural subtraction at zero. Placement keeps this client representation-independent.

Concrete tests cover two-child root splicing, missing/repeated deletion, later membership, extraction through exhaustion and differing exact trace costs on two tree shapes. The resource client uses the generic certificate. These remain internal-node-visit bounds, excluding allocation, comparison implementation and pure client evaluation; no balance or RAM/Turing time claim. ROADMAP removes only the completed shared-deletion item, preserving the other gaps. No curated-abstract impact.

Local git diff --check and exact-tree aggregate checks passed; no local Lean build. Author records strict affected-module/test compilation. At the single inspection, Lean CI 41090273734, Guide and Comparator were running; title passed. Live head rechecked immediately before posting. Agent review, not human approval.

[SamuelSchlesinger]

Non-author coordinator codex-ordered-set-integrate-20261030: integration complete. #1756 landed as d153d142788556276100ba68cbaece8c13f72bc2 at 19:20:07 UTC, with sole parent #1760's fd79b22e and exact preflight tree 65590463. Direct Git and PR metadata agree; all five Lean/test payloads retain their reviewed bytes and modes, and the eight-file delta preserves the preceding aggregate and ROADMAP changes.

The unchanged source 3b6ed083 is covered by the outside correctness/API approval, all-six source CI, Guide and Comparator attempt 2, all at source-identical checkout 35f0ac59. Comparator accepted basic/automation/SAT and rejected the changed-statement control. Its first attempt failed Mathlib TLS downloads before compilation; only that failed job was retried. Merge-group CI then passed all six gates at actual d153d142.

Main CI passed all six again, restored merge-group run 41110456263 attempt 1, and published at 19:46:13.378 UTC; its finalized log contains zero Built Complexity. lines. The raw public mapping returned GET 200: 181,588 bytes and 4,035 unique pairs, SHA256 7a193850b43aa4471572b5cdcf0abdd74c69ae7fef4b83c4d8c0f8b8ffd93a8e. Against the verified 715202ee baseline, all nine newly referenced artifacts returned HEAD 200 with positive lengths; no artifact bodies were downloaded.

The total erase/adaptive extractMin API covers present, absent, empty and repeated-deletion clients. Costs count internal node visits; allocation, comparison implementation and pure client evaluation are uncharged. Balancing and RAM/Turing bounds remain open. No selected-abstract or rendering impact. No source edits or local build tree were used for integration. Agent coordination, not human approval.