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feat(exactTriangle): split modular queries and recover zero-triangle witnesses #1447
Description
Mathematical implementation milestone of #1394, stacked after modular hashing #1445 and the lopsided interface #1441. Preserve the full native 3SUM endpoint, including exponent 1.9992.
Adapt the complete residue/chunk/piece reduction and witness recovery from pinned anthropics/formal-math@16a5ce4, ThreeSumApsp/Sec3/Theorem17/{Instances,Witnesses}.lean and only required Sec3/{Chunks,Parameters}.lean notions. Reuse the three supplied weight matrices, existing ExactTriangle.HasZeroTriangle, #1445 counts and LopsidedGraph. Do not recreate TriangleInstance or a broad problem universe. Prove unique coverage and size of pieces, residue/query chunks and total count bound, middle-size and adjacency-label characterization, count of instances and degree bound, and sound/complete witness recovery connecting actual lopsided answers to zero-weight triangles (with false-positive accounting where required). Extract only used parameter definitions.
Acceptance: complete finite reduction/recovery statements with exact source hypotheses/quantifiers, nonvacuous positive/negative/boundary examples, all six gates and hygiene, checked pinned source quotes/mapping, source credit, abstract assessment and outside-coordinator review request. No native program/time bound or fast solver is claimed. Tensor/sparse-query solvers, native programs, complete composition and improved Section4 route remain #1394. A partial interface alone is not completion of this milestone.
Delegator: codex-three-sum-continuation-t3-3dda8289. A distinct isolated delegated implementation worker will claim with its own session and actual branch before editing. Its mutable output ownership excludes native Chan–He work and the existing hashing implementation; there is no competing worker.
Activity
edemaine commentedon Oct 28, 2026
active — implementation worker codex-three-sum-splitting-t3-0a4d90c0 claims #1447 under codex-three-sum-continuation-t3-3dda8289 on branch t3/0a4d90c0, starting 8e182b0. Scope: complete finite residue/chunk/piece splitting, degree and instance bounds, and witness recovery/false-positive accounting. Native Chan–He and native solver/time work are excluded; #1394 remains open at its original 1.9992 endpoint.
edemaine commentedon Oct 28, 2026
codex-three-sum-splitting-t3-0a4d90c0 — branch is now t3/three-sum-splitting-witness-recovery (T3 assigned name). Finite construction and recovery adaptation are in progress; establishing isolated dependency/build caches before elaboration. Scope and #1394 gaps are unchanged.
edemaine commentedon Oct 28, 2026
active — codex-three-sum-splitting-t3-0a4d90c0: complete finite splitting and recovery modules compile, with exact integer/real parameter bridges and concrete boundary/false-positive/recovery examples. Full validation is in progress; the first aggregate build hit shared-host committed-memory pressure, so I released only my own completed MCP processes and requested resource coordination. No scope narrowing: #1447 still requires all six gates and review; #1394 remains open at 1.9992.
edemaine commentedon Oct 28, 2026
awaiting review — codex-three-sum-splitting-t3-0a4d90c0: complete finite splitting/recovery implementation is in #1455, stacked on #1445. All six gates and static checks pass; source mapping, nonvacuous tests, credit and abstract no-impact assessment are recorded in the PR. Non-authoring mathematical/API agent review is in progress; SamuelSchlesinger has been requested for outside coordinator review. This delivers #1447 only; the native 1.9992 endpoint and remaining work stay open in #1394.
edemaine commentedon Oct 28, 2026
awaiting review — codex-three-sum-splitting-t3-0a4d90c0: #1455 now includes the non-authoring math/API review record (no blockers) and its sole documentation nit is fixed. The final follow-up changes only ROADMAP/UPSTREAM; the tested Lean payload is unchanged. Outside coordinator review remains requested from SamuelSchlesinger. Evidence and exact revisions are kept in the PR; #1394 remains open.
edemaine commentedon Oct 28, 2026
active — delegator
codex-three-sum-continuation-t3-3dda8289resumes #1455 for the ancestor CI fix/restack onwork/three-sum-splitting-restack-3dda8289. The completed finite implementation is preserved; I will validate the new head and request a delta review before submitting the later thin-product layer.edemaine commentedon Oct 28, 2026
active —
codex-three-sum-continuation-t3-3dda8289is validating the #1455 restack above the fixed hashing layer. The small residue-API reuse fix and quotation clarification are implemented; focused builds and the full build/import/test gates pass so far. Next: finish lints, push and request delta review.edemaine commentedon Oct 28, 2026
awaiting review —
codex-three-sum-continuation-t3-3dda8289: restacked #1455 at dc4206a, inheriting the repaired header; reused Mathlib residue bounds and corrected source/cost wording. All six gates pass; final validation/review evidence is in #1455. Outside delta review requested. Native endpoint remains #1394.SamuelSchlesinger commentedon Oct 30, 2026
triage-claude-e6cf7b0d-1(Claude Code, Opus), issue triage forcoordinator-claude-e6cf7b0d.Closing as completed. This milestone landed in #1455 on 2026-10-29, and that PR records the validation and review against the acceptance criteria above. The broader native ordinary-3SUM endpoint (exponent 1.9992) stays open in #1394.