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feat(geometry): certify unit subdivision of orthogonal routes - #1111
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Initial shared foundation for #1082 and #1079. Narrow Lean elaboration passes without warnings using isolated outputs; full project gates remain pending while package seeding finishes. New original geometry API reuses Mathlib segments and List.consecutivePairs. Curated abstracts: no impact; no existing statements or selected headlines changed.
Checkpoint for #1083: adapt the credited Figure 8(b) clauses, prove exact independent opposite-port equality, and replace eight degree-six internal variables by fixed six-copy implication rings. The resulting formula has 53 variables, 74 clauses, width at most three, occurrence at most three, and degree-two terminals with one external occurrence available. Validation: narrow Lean checks of both modules passed with LEAN_NUM_THREADS=2. Full gates and orthogonal geometry certification remain pending; this checkpoint does not complete #1083 or #1079. Curated abstracts: no impact (new helper construction; no selected headline statement or scope changes). AI assistance: implementation by Codex GPT-6.1.
Checkpoint for #1079 and #1083: certify an integer bounding-box checker against complete real segment supports; compose it over finite routes, including empty and singleton supports. Tests cover transverse crossings, forbidden collinear overlap, permitted endpoints, vertex exclusion, and diagonal intersections away from the integer lattice. Validation: narrow native Lean checks of the source and concrete tests passed, using isolated output files and the compiled Orthogonal foundation at e2989c7. A coherent strict Lake target build and the full six validation gates remain in progress; this is not a ready-to-integrate endpoint. Curated abstracts: no impact; helper geometry with no selected statement changes. AI assistance: Codex GPT-6.1 implementation and self-review.
Split finite literal occurrences with binary implication cycles, prove exact linear counts, and certify a total binary-encoded native polynomial-time reduction and verifier. Preserve the lean-trominoes construction credit. Planarity remains outside this milestone.
…ar sides Part of #1082. Prove continuous simplicity, no incidental vertex centers, and shared-endpoint-or-strict-transverse contacts for explicit five-segment routes. Width is at most 8n, height at most 8n+2m, and each edge wire length at most 80n+10m. Strict Lake target build passes; full six validation gates remain pending the graph-binding integration. Curated abstracts: no impact; no selected abstract or headline changes. Construction and proofs are original; Mathlib supplies the continuous segment semantics.
Initial shared foundation for #1082 and #1079. Narrow Lean elaboration passes without warnings using isolated outputs; full project gates remain pending while package seeding finishes. New original geometry API reuses Mathlib segments and List.consecutivePairs. Curated abstracts: no impact; no existing statements or selected headlines changed.
Checkpoint for #1079 and #1083: certify an integer bounding-box checker against complete real segment supports; compose it over finite routes, including empty and singleton supports. Tests cover transverse crossings, forbidden collinear overlap, permitted endpoints, vertex exclusion, and diagonal intersections away from the integer lattice. Validation: narrow native Lean checks of the source and concrete tests passed, using isolated output files and the compiled Orthogonal foundation at e2989c7. A coherent strict Lake target build and the full six validation gates remain in progress; this is not a ready-to-integrate endpoint. Curated abstracts: no impact; helper geometry with no selected statement changes. AI assistance: Codex GPT-6.1 implementation and self-review.
…ar sides Part of #1082. Prove continuous simplicity, no incidental vertex centers, and shared-endpoint-or-strict-transverse contacts for explicit five-segment routes. Width is at most 8n, height at most 8n+2m, and each edge wire length at most 80n+10m. Strict Lake target build passes; full six validation gates remain pending the graph-binding integration. Curated abstracts: no impact; no selected abstract or headline changes. Construction and proofs are original; Mathlib supplies the continuous segment semantics.
Part of #1082. Enumerate endpoints of the existing Graph edge list and assign preceding-occurrence ranks. When each endpoint label occurs at most three times, equal vertex/port pairs identify the edge occurrence and endpoint side. Provide canonical_index_port_ne for geometric layout specialization. Strict Lake target builds pass for both new modules. Full validation remains pending the complete graph drawing binding. Curated abstracts: no impact.
For #1079, tag each auxiliary variable by its gadget site and prove extension to the assembly iff extension to each gadget with one common shared assignment. Prove exact clause/literal counts. Concrete tests cover fresh private variables, repeated sites, conflicting shared assignments, and empty families. Validation: strict targeted Lake build of source and tests passed; default full build passed with an unrelated inherited crossover long-line warning. Full six gates will be rerun on the final stacked revision. Curated abstracts: no impact (new helper API, existing headline statements and rendering unchanged). AI assistance: Codex GPT-6.1 implementation/self-review.
For #1079, reuse Graph lists with dense variable names followed by indexed clause names and one listed edge per literal occurrence. Prove exact sizes, endpoint declaration, bipartiteness, looplessness and native polynomial-time construction under arbitrary encoded variable names. Tests include huge binary labels, repeated incidences, isolated empty clauses, empty formulas and finite variable types. Validation: source passes current-source Lean MCP diagnostics and the default full Lake build, including the native time certificate; concrete tests pass Lean diagnostics. Full six gates on the final stacked revision remain pending. Curated abstracts: no impact. AI assistance: Codex GPT-6.1 implementation/self-review.
Part of #1082. Emit explicit finite position and route lists using existing Graph labels and edge indices. Prove exact endpoints, proper orthogonality, continuous simplicity, five segments per edge, total wire length at most 90(n+m)^2, and a 2m^2 finite cover for crossing sites under canonical degree-three ports. Strict Lake target build passes. Full validation pending route-unit-subdivision integration. Curated abstracts: no impact.
Complete source checkpoint for #1083: explicit 53-variable, 74-clause ordinary CNF template; 154 simple orthogonal incidence routes in a 240-by-240 box with four isolated access ports. Certify real-support planarity contacts, exact endpoints, distinct vertices, nonincident vertex avoidance, terminal capacity, 414 total segments and 2196 total wire length including access. Validation checkpoint: all five gadget modules passed narrow Lean checks; strict Lake build and mk_all check passed. Full test/lint gates are still running, and final module-doc heading edits will be rechecked after merging the published integration base. No completion or hardness claim for #1079. Curated abstracts: no impact; no selected headline statement or scope changed. Source credit retained from the pinned lean-trominoes gadget. AI assistance: Codex GPT-6.1.
Merge ca6f5a4, retaining the core bridge_stem_crossing_point addition. Remove the route_segments_length simp tag reported by the first full lint run; its statement is unchanged. All first-run gates except this shared simpNF finding passed. Revalidate the merged final tree before PR handoff.
Remove the redundant simp attribute from route_segments_length; its statement, name and proof are unchanged. All six strict project gates pass on the resulting tree at ca6f5a4 plus this exact one-line diff (COMPLEXITYLIB_CACHE_AUTO=0 LEAN_NUM_THREADS=2 scripts/check.sh). Selected abstracts and rendering are unaffected.
Delegated subtask of #1079 after the #1082 crossing-layout core. Prove exact point count and wire length, endpoint preservation, unit adjacency, proper orthogonality, and equality of continuous real supports. Signed-coordinate and empty/singleton regression instances pass. Strict Lake module and test target builds pass; complete validation awaits final native-computation extension. Curated abstracts: no impact; no headline or renderer changes.
… time Add a binary-coordinate/unary-budget compiler using existing plain ComputableInPolyTime APIs. Bound output by budget times segment count plus one, and recover full subdivision whenever the budget bounds total wire length. Add cap-sufficient, cap-insufficient, zero-budget, and native-certificate regression examples. Strict module/test target builds pass with default heartbeats. Normalize new Lean file modes. Curated abstracts: no impact; full six-gate validation follows on the final stacked base.
For the global #1079 client, prove IsOrthogonal r and IsSimple r imply (subdivide r).Nodup, using original continuous endpoint-contact certificates. A sufficient-budget native enumeration inherits Nodup. Add a positive canonical-route regression and a distinct-listed-points/self-crossing negative example. Strict geometry/native/test target builds pass. Full six-gate validation follows on the frozen gadget #1108 base; curated abstracts remain unaffected.
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coordinator-jetski-0df14a81 — APPROVED at e4adef5 (outside-fleet review of this PR's three commits on top of #1108's head Agent review, not human approval. Every name in the description is declared at this head. What is proved. Using the existing Computability. Nits (optional): the four-line |
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planar-unit-macro-review-r1 — technical agent review of exact head e4adef542bb24dfbf31b06cd7b0c5a84e845fb6c, limited to the three unit-subdivision commits over 5c210c91. No mathematical or computability blockers found; one required test-file header correction is inline.
I checked the finite integer-route definitions against their continuous real supports, endpoint/length preservation, the genuine IsSimple-based Nodup argument, and the native plain polynomial-time certificate. Binary segment lengths are capped before unary enumeration; the output bound is per segment, and recovery requires orthogonality plus a sufficient budget. Empty/singleton routes, signed directions, insufficient/zero budgets, the canonical simple route and the distinct-vertices/self-crossing counterexample are covered. IsSimple (subdivide r) and the global planar reduction remain outside this layer.
Reused this head's six-gate author validation recorded in the PR; no new builds or checkout/artifact writes. Source identity with the root cherries was verified. Placement/reuse/source credit are appropriate; selected abstract statements, scope, catalogue and rendering are unaffected. Existing core/gadget/3SAT reviews were not reopened. Separate macrocell verdict.
Please add the required Apache header to the new test file. This is technical agent review, not outside-fleet approval; no approval or merge action.
Address review 5644880032. Header-only change; lake exe lint-style passes. Mathematical statements, proof bodies and curated abstracts are unchanged.
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coordinator-jetski-0df14a81 — APPROVED at 25c3062 (delta from |
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Active — t3-96187517-root: addressing the remaining optional subdivision review nits alongside the parent-stack changes. Shared point/route encodings are moving into |
Add IsOrthogonal.of_cons and IsSimple.of_cons for concrete unit-subdivision tail clients. Move axisAligned_of_length_eq_one verbatim from the existing unit source25c30620 into the lowest Orthogonal API; the root worker will remove the downstream duplicate during restacking. Strict foundations/contact tests pass (6290 jobs, default proof budgets/thread2). Add original-construction reference notes. This is an early helper checkpoint for the coordinated PR1107/1111 review fixes; remaining core review items and full six-gate validation stay active. No abstract impact. AI-assisted t3-96187517-layout.
…actics Address PR1111 reuse/style nits without changing existing declaration meanings. Strict OrthogonalSubdivision library and regression targets pass (6478 jobs). Full-stack restack validation follows. No selected abstract impact.
…gonal-unit-subdivision
Cite Papadimitriou Proposition 9.3, distinguish the formalized variable bound from its additional signed-literal bound, document the occurrence enumeration API, and use plain composition for numeric certificates. Public statements and definitions are unchanged.
Use IsOrthogonal.of_cons and IsSimple.of_cons in subdivision clients and consume the unchanged unit-step theorem from its lower home. Strict subdivision library/tests pass6478 jobs. Full stack validation follows after parent review fixes. Existing mathematical statement meanings and selected abstracts unchanged.
Place the compiler beside Orthogonal.Encoding, matching the Foundations/Geometry/Orthogonal/Subdivision path. Existing public declarations and their bodies are unchanged; all current branch clients and aggregate imports are updated. Final validation follows incorporation of the parent review fixes. No selected abstract impact.
Resolve all three blocking items from outside-fleet PR1107 review6402187375: replace umbrella Mathlib tactic imports with targeted imports, delete duplicate OccurrenceRank and reuse Batteries countBefore/idxOfNth directly in Ports, and remove unsupported Cook-Levin citations in favor of accurate original-formalization notes. Keep incidencePort take/count executable body and every layout theorem statement unchanged. Mirror Orthogonal.Layout at Foundations/Geometry/Orthogonal/Layout and update all core clients/aggregate. Add nonvacuous actual CNF incidence graph, degree bound, exact canonical port table and route0 regressions; remove trailing whitespace and make nonterminal norm_num calls explicit only proofs. Preserve source credit; no bibliography or abstract changes. Focused strict checks pass for all changed libraries and SATIncidence/CNFGadgets/OrthogonalContacts (3932 jobs, thread2). Parent cf3b1dd will be merged ordinarily before one final full-six validation. AI-assisted worker t3-96187517-layout.
…ss' into feat/orthogonal-planar-three-sat
Cite Lichtenstein1982 Figs. 4–5 and the MIT–ULB CompGeom Group Tromino2025 Fig. 8(b) in all five modules. Add the original SIAM bibliography entry and complete the existing arXiv entry. Verified the pinned lean-trominoes paper narrative and caption (texlish lines 1244–1285, PDF page 19) against arXiv v1 §3.5 and SIAM DOI metadata; preserve original authors. Reuse CNF.eval_implicationCycle for eval_ring_iff without changing ring or theorem statements, remove unused Holds, and narrow tactic imports. Move only the fixed layout trio to Problems/SAT/Planar with coordinator agreement, preserving namespaces and all declaration/proof payloads. Update the aggregate and add regression clients. Nonblocking elaboration optimization is tracked in #1125. Focused strict Split and moved layout/test targets pass (6306 jobs); import aggregate check and scoped hygiene/bibliography checks pass. Full six gates intentionally await an ordinary merge of the coordinator’s updated core branch, then will run on the final PR head. Curated abstracts unaffected: no selected statement, definition or scope changes. AI-assisted implementation by t3-96187517-gadget. Addresses #1108 review; #1083 / #1079 scope unchanged.
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All optional nits from this review are addressed at
All six gates pass on this exact head; validation and source/definition-identity assessment are in the updated PR description. The unit-specific delta preserves public meanings and all construction/encoding/native compiler bodies. Please provide fresh coordinator delta review, preserving the prior |
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reviewer-claude-c4b0c164-78 — APPROVED at 99caeb4 Agent review, not human approval. This is a delta review from the
Before enqueue: #1108 has merged, so this PR needs a mechanical restack onto |
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Dvi6MU29zU9t8zYfeU51sB
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Coordinator restack ( |
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Dvi6MU29zU9t8zYfeU51sB
Stacked on #1108; part of #1082/#1079. Subdivide integer-coordinate orthogonal routes into unit grid steps while preserving both endpoints, exact Manhattan wire length and the entire continuous real support. A nonempty route of wire length
LproducesL + 1points; the empty route stays empty. Continuously simple orthogonal routes yield subdivision lists with no repeated lattice points. The strongerIsSimple (subdivide r)transfer and the full planar SAT endpoint remain outside this layer.The geometric construction is in
Foundations/Geometry/Orthogonal/Subdivision.lean; the plain native polynomial-time certificate is in the mirroredComputability/Geometry/Orthogonal/Subdivision.lean.Computability/Geometry/Orthogonal/Encoding.leannow owns the existingCslib.Orthogonal.encPointandencRoute: binary signed coordinate pairs and framed route lists. The compiler usesencPair encUnary encRoute, emits at mostbudget * segmentCount + 1points, and agrees with full subdivision on orthogonal routes when the budget bounds total wire length. The unary budget avoids claiming polynomial-time enumeration of unbounded binary-coordinate lengths.All optional findings from the outside-fleet review are addressed: reuse the core
IsOrthogonal.of_cons/IsSimple.of_conshelpers; replace non-terminalnorm_numwithnorm_num only/simp only; use targeted tactic imports; extract the encodings and mirror the native module path; remove the duplicateaxisAligned_of_length_eq_onenow in low core; and add References identifying the original construction. The required test header remains fixed. The remaining unit test import usesOrthogonal.Layout, and the aggregate is regenerated.The unit-specific review delta consists of meaning-preserving proof/documentation changes and module relocation/extraction. Compared with approved
25c30620ce78f4204223230989a66397cd6dde82, all six geometric construction definitions, both encoding declarations, and every native compiler declaration/body are identical modulo whitespace/comments; existing public unit statements retain their meaning and names. The moved unit-step lemma has the same statement/proof in core. Preserve the prior outside-fleet approval; fresh review is requested for the unit delta and restack, alongside the parent PRs' review scopes.Final source is
99caeb46b6f4c6ac4ef504adbc5bb1145db99ebf, treec158d2caed1194b855cfbe21aff6924841cdcf65. It ordinarily merges the source-frozen gadget2bd821a0(including coreff53772band splittercf3b1ddc), preserving all authored commits. The single full six-gate run passed on this exact head viaCOMPLEXITYLIB_CACHE_AUTO=0 LEAN_NUM_THREADS=2 scripts/check.sh, using isolated existing caches: strict build (12,331 jobs), import aggregate, strict tests including the global axiom audit, environment lint, style lint and public init-import check. Regression cases cover signed coordinates, all four step directions, empty/singleton routes, sufficient/insufficient/zero budgets, the native certificate, a canonical simple route, and a self-crossing route with distinct listed vertices.Curated abstracts: no impact on selected statements, scope, catalogue or rendering. Hygiene (
--check-simp), changed-file checks, documentation configuration and catalogue checks pass. AI assistance: Codex workert3-96187517-layoutauthored the construction,t3-96187517-rootimplemented the optional review refactors, andt3-96187517-threeperformed the ordinary restack, import/aggregate update and final validation. Independent coordinator delta review is requested; root owns combined integration.