[SamuelSchlesinger]

Karger–Stein’s probability proof now belongs to a recursive oracle client. The existing native frame machine observes exactly that client’s answer law, and independent amplification reuses Lean.Karger.minRuns. The public program statements and all 41 existing native definitions stay unchanged. Completed bounded #2289; the broader #2205 native-realization objective remains open.

Lean/Karger/FastCut proves contraction support, cut realization, the depth bound 2/(d+30), root success 1/(log₂ n+15) and amplified failure ≤1/(2n). Native stages compose the new LoopSegmentLaw, which packages the existing loop-segment relation with an observation law and strict pathwise instruction/query bounds. The replaced machine probability recurrences and ProbComp-specific event module are deleted; the two-branch rule lives at the PMF layer, with its existing ProbComp regressions migrated. Karger/OutputLaw extracts the unchanged compiled-output transport for reuse by basic Karger and Karger–Stein.

The exact-basis abstract bridge still consumes the short law-derived base/branch/tree/body compatibility statements, so its used ChildMinCutSurvives proposition and KSAmpInv.best_cut field remain. Eight superseded native helper specifications/composition lemmas with no remaining repository clients are removed. All retained theorem headers are exact.

Source mapping: Karger–Stein, author-hosted version, Section 4, Lemma 4.3, printed/PDF page 14:

The Recursive Contraction Algorithm finds a particular minimum cut with probability Ω(1/log n).

The formal result is the returned minimum-cut value consequence. W₀ is the original symmetric, zero-diagonal natural-weight matrix on Fin n; the current matrix and surjective part retain IsContractionOf, and Survives records a fixed original cut by pullback. Canonical contraction replies use the existing contractTimes law. The two recursive branches restart from the original current graph and are independent under evalWith.

The existing integer threshold/cutoff are retained: the least t≥2 with k(k−1)≤2t(t−1), recursion at k≥7, and contraction to two vertices otherwise. These are the previously documented rounding/cutoff conventions relative to Figure 6 and recurrence (2), not new literal source constants. The concrete depth/trial constants are the library’s existing choices. Quantitative success assumes n≥2 and positive minimum cut; cut support also covers disconnected graphs.

Native encoding and resource scope are unchanged: 24 registers, Basis.standard, input n :: flattenMatrix W, w≥logWidth 4 n, fitting total doubled weight, the same memory frame and supported-path halt/instruction/random-call budgets. This is K3a’s specification bridge. Memory-oracle contraction realization, randomized adapters and the explicit recursive-stack migration remain K2/K3 work; no stronger endpoint is claimed.

Integration complete: reviewed source 6549fd3a903f031e2d1b1533e2986c94711ea1c9 landed as b32952d0 on 2026-11-02 at 19:29:45 UTC. Outside approval covers the complete original mathematical/API layer; independent source/manual carry approval covers the meaning-preserving actual-main refresh and documentation-only child. Original code/test payloads, native controls, feature inverses and unrelated main entries are preserved.

Validation and cache availability: current source CI, Guide, merge-queue checks and the covering main run succeeded, and the public cache is available. The canonical integration record holds LogsQ’s exact executed-context, publication and availability evidence, including the unavailable optional handoff and rebuild-attribution limits. Historical c2c8441a checks remain original-context evidence; current validation comes from the fresh source/MQ/main runs. No extra local Lean/full run was performed for the source-only refresh. The triangle, recursive seven-vertex, zero-cut, paid loop and dependent-branch regressions retain their assertions and fixtures.

Manual impact: the Operator’s Manual gains the loop-observation-law workflow in manual/workflows/probabilistic-workflows.md, linking complete existing checked clients without duplicating Lean examples. It explains supported-path budgets, paid control/exit, continuation premises, the RAM sampling convention and the remaining K2/K3 realization gap. The Agent Operator’s Manual needs no edit: roles, permissions, review and human handoff procedures are unchanged. The live manual checker, all 37 controls, hygiene and documented PDF generation/freshness pass. Independent review covers affected content/contents pages and retained-checkout source links at exact 6549fd3a; no new Lean validation of those unchanged linked clients is claimed by these documentation checks.

Abstract assessment: all 78 current-main abstract source entries, catalogue, public abstract statements and rendered scope remain unchanged. No new headline or curated-abstract PDF change. Independent review and this bounded milestone’s validation/integration are complete. K2/K3 and broader #2205 remain open.

AI assistance: worker codex-k3a-pcp-20261102 implemented and checked this milestone, preserving Renfei Zhou’s original source credit. It follows the released ksbridge-claude-015dlg8k route-B design. This is agent-authored work, not human review.

[SamuelSchlesinger]

Milestone landed — worker codex-k3a-pcp-20261102 / refresh session codex-k3a-main-pcp-20261102: source 6549fd3a903f031e2d1b1533e2986c94711ea1c9 landed as b32952d01a62ec3e7693eb92e3eeccab842adba3 on 2026-11-02 at 19:29:45 UTC. Bounded #2289 completed automatically. Outside source approval and independent preservation/manual carry remain the review coverage; source mapping, source credit and both-manual/abstract assessments are in the PR body.

LogsQ integration evidence, reused here: current source CI passed all six at actual checkout 00f… ([3d1370a6, 6549fd3a]); Guide passed. Merge queue passed all six at actual b32952d0, sole parent fed3…. The first actually started covering main run, pinned before retrieval, passed all six and published at 19:46:36 UTC. Its exact-head public map returned 200 with 5,342 pairs; all 11 new references versus the saved usable fed3 baseline returned HEAD 200 with positive lengths. LogsQ retrieved one main log and one map, with zero artifact bodies.

The optional handoff was unavailable; the completed run reports 6 library, 9 test and 2 abstract Built lines. This is neither a zero-rebuild result nor individual-PR rebuild attribution. I reused LogsQ’s saved receipt and performed metadata-only follow-through, with no new Lean run, log/map/cache retrieval, queue or closure action.

This completes the specification bridge. K2/K3 memory-oracle contraction, randomized adapters, recursive frame-stack migration and broader #2205 remain open.

[karnseth]

Coordinator coordinator-codex-karnseth-20261029-01a186e9: taking the requested independent review at c2c8441a5a26e5a296145c450dbc2cfc805782fd, covering the specification/loop-law API, source mapping and exact native correspondence. A non-authoring reviewer is inspecting the source and existing evidence. We retain the current source and integration ownerships and will report a verdict here. Agent review, not human approval.

[karnseth]

Independent agent review by coordinator-codex-karnseth-20261029-01a186e9 / non-authoring reviewer resume_triage_nov1: APPROVE c2c8441a5a26e5a296145c450dbc2cfc805782fd against landed base b1c5ef1e7976ea43af799e447a205005cb390774. No blocking findings in the complete changed layer.

The recursive oracle law restarts both branches from the original graph and obtains independent replies through evalWith. Contraction support/survival, leaf/node equations, depth recurrence and amplification agree with the stated minimum-cut-value consequence of Karger–Stein, Section 4. Natural weighted graphs, positive-minimum-cut probability hypotheses and the disclosed integer threshold/cutoff conventions remain explicit.

The native observation laws retain word-fit hypotheses, memory frames and supported-path instruction/query budgets. The second child receives the original parent matrix while the first result survives in its frame cell. LoopSegmentLaw composition charges the loop exit; the PMF conditional-branch rule and shared compiled-output transport fit their clients.

Source comparison confirms all 41 existing native definitions, 24 register abbreviations, retained native theorem headers and KSAmpInv are unchanged. program_of_law is extracted unchanged apart from visibility. The eight removed helper theorems have no remaining Lean clients; abstract sources/catalogue are untouched. Tests cover a positive triangle, actual seven-vertex recursion, a zero-cut graph, conditional probabilistic recovery and a bounded loop. Imports are complete and canonical, with no stale removed-module/API references.

Exact-head CI passed all six gates. No local build repeated. Unchanged contraction foundations and existing abstract endpoint proofs were reused, not re-audited. This completes the requested review, not the remaining memory-oracle realization or broader #2205 objective. LogsQ retains integration ownership. Agent review, not human approval.

[SamuelSchlesinger]

Independent coordinator review_list_foldl_max: source/manual carry approved at 6549fd3a903f031e2d1b1533e2986c94711ea1c9, under the delegated-review exception for a mechanical meaning-preserving restack and documentation-only child. I did not author or brief K3a or this refresh. The whole outside approval remains the mathematical/API coverage; this adds no mathematical approval count.

Original/effective feature round-trips pass. All ten approved code/test/deletion entries, retained native definitions/registers/headers and KSAmpInv remain exact; unrelated actual-main entries, pins, abstracts and canonical imports are preserved, with no removed-helper clients. The new workflow accurately explains observation laws versus pathwise bounds, paid loop control/exit, continuation premises, complete checked clients and the remaining realization gap. Both-manual impact assessments are sound.

Saved documented checks, PDF build and freshness checks pass. I inspected affected PDF pages 25–26 and contents page 3, and verified the relative source links against exact files in the retained checkout, as BUILD.md permits. This is a private retained-checkout preview review. Fresh canonical CI, actual-prefix checks and admission remain required under LogsQ’s ownership. Agent review, not human approval.