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package for AutoContext-assisted Erdős-style formal math problem loops with Lean verification.","maintainers":[{"name":"jayscambler","email":"jay@greyhaven.ai"}],"readme":"# pi-autocontext-erdos\n\nPi package for AutoContext-assisted Erdős-style formal math problem loops with Lean verification.\n\nRelease notes live in `docs/RELEASE_<version>.md`, with machine-readable release evidence under `docs/release-evidence/`.\n\nThis package is an orchestration layer. It does **not** replace Lean and does **not** claim to prove open problems. It helps structure a math exploration loop: problem intake, formalization, lemma planning, proof attempts, Lean-backed verification, and reporting.\n\n## Relationship to `pi-autocontext-lean-verify`\n\nUse this package for the problem loop and research workflow:\n\n```text\npi-autocontext-erdos\n  = problem intake + formalization + lemma ladder + attempt logs + reports\n```\n\nUse `pi-autocontext-lean-verify` as the verifier/proof-repair backend:\n\n```text\npi-autocontext-lean-verify\n  = Lean oracle + fixed-template proof-body repair + guardrail checks\n```\n\nInstall both when you want proof-repair automation:\n\n```bash\npi install npm:pi-autocontext-lean-verify@0.1.17\npi install git:github.com/greyhaven-ai/pi-autocontext-erdos\n```\n\nFrom a local checkout:\n\n```bash\npi install ./pi-autocontext-erdos\n```\n\nFor local development, from this checkout:\n\n```bash\nnpm install\nnpm run validate\nnpm run pack:dry-run\npi install ./pi-autocontext-erdos --local\n```\n\n## Provided resources\n\n- Extension tool: `autocontext_erdos`\n- Skill: `erdos-math-loop`\n- Prompt template: `erdos-math-loop.md`\n- Domain notes: `docs/DOMAIN.md`\n- Validation notes: `docs/VALIDATION.md`\n- Lake/Mathlib verifier notes: `docs/LAKE_MATHLIB_SUPPORT.md`\n- Mathlib benchmark evidence: `docs/MATHLIB_BENCHMARK.md`\n- Final theorem audit guardrails: `docs/THEOREM_AUDIT.md`\n- Reusable bounded artifact schemas and validator: `docs/SCHEMAS.md`\n- Benchmark registry: `benchmarks/index.json`\n- Release process and evidence cross-checks: `docs/RELEASE_PROCESS.md`\n- Lemma graph orchestration: `docs/LEMMA_GRAPH.md`\n- Erdős–Straus parametric family benchmark: `docs/ERDOS_STRAUS_PARAMETRIC_FAMILIES.md`\n- Erdős–Straus bounded certificate-search benchmark: `docs/ERDOS_STRAUS_BOUNDED_SEARCH.md`\n- Erdős–Straus bounded-search stress benchmark: `docs/ERDOS_STRAUS_BOUNDED_STRESS.md`\n- Schur lower-bound bounded certificate benchmark: `docs/SCHUR_LOWER_BOUND_BOUNDED.md`\n- Van der Waerden lower-bound bounded certificate benchmark: `docs/VAN_DER_WAERDEN_LOWER_BOUND_BOUNDED.md`\n- Example runs:\n  - `examples/erdos-ginzburg-ziv-n2`\n  - `examples/erdos-ginzburg-ziv-n3`\n  - `examples/schur-two-color-n5`\n  - `examples/schur-two-color-n5-lemma-graph`\n  - `examples/schur-two-color-lower-bound`\n  - `examples/van-der-waerden-3term-lower-bound`\n  - `examples/mathlib-divisibility-prime`\n  - `examples/erdos-straus-parametric-families`\n  - `examples/erdos-straus-bounded-search`\n\n## Example validation\n\nThe checked examples include the `n = 2` and `n = 3` finite instances of the Erdős–Ginzburg–Ziv theorem over natural numbers, plus a full-pipeline finite Schur two-color `n = 5` benchmark. The `n = 2` EGZ example proves:\n\n```lean\ntheorem egz_two_nat (a b c : Nat) :\n    (a + b) % 2 = 0 ∨ (a + c) % 2 = 0 ∨ (b + c) % 2 = 0\n```\n\nThe harder EGZ `n = 3` example proves that among any five natural numbers, one of the ten triples has sum divisible by `3`. The AutoContext repair smoke in `docs/EGZ_N3_AUTOCONTEXT_REPAIR.md` deliberately breaks that proof, repairs it back to a Lean-verified candidate with `autocontext_erdos`, and the compact repaired proof is now the canonical example.\n\nThe Schur `n = 5` example proves the finite two-color statement that every coloring of `1..5` contains a monochromatic `x + y = z` triple. It exercises direct Lean verification, `audit_theorems`, fixed-template export, and `pi-autocontext-lean-verify` handoff; see `docs/SCHUR_N5_FULL_PIPELINE.md`.\n\nThe Schur lower-bound bounded example emits explicit two-coloring certificates for `2 ≤ n ≤ 4`, including the finite witness `S(2) > 4`, using the reusable bounded artifact schema with a non-Erdős–Straus certificate payload; see `docs/SCHUR_LOWER_BOUND_BOUNDED.md`.\n\nThe Mathlib divisibility-prime benchmark imports `Mathlib` in a Lake project and proves a scoped Euclid-lemma API theorem using `Nat.Prime.dvd_mul`; see `docs/MATHLIB_BENCHMARK.md`.\n\nThe Erdős–Straus parametric-family example verifies only the elementary even-denominator family as a rational identity over `ℚ`; it is explicitly not a proof of the full conjecture. It exercises Lake/Mathlib verification, lemma graph frontier tracking, `audit_theorems`, fixed-template export, and graph result recording; see `docs/ERDOS_STRAUS_PARAMETRIC_FAMILIES.md`.\n\nThe Erdős–Straus bounded-search example generates exact certificates for `2 ≤ n ≤ 100`, emits them as chunked Lean certificate modules plus aggregate `generatedCertificates` data, proves reusable Boolean integer-checker soundness, proves checker-pass/validity/local chunk coverage/hierarchical aggregate coverage theorems, then derives the public finite theorem from those checker theorems in Lean/Mathlib. The JavaScript search is only a candidate generator; Lean remains the correctness oracle. The generator supports `--min`, `--max`, `--lean-chunk-size`, `--check`, reusable bounded artifact schemas, an artifact integrity manifest, and `npm run validate:generated`; see `docs/ERDOS_STRAUS_BOUNDED_SEARCH.md` and `docs/SCHEMAS.md`. Out-of-band stress benchmarking through `npm run stress:erdos-straus-bounded` supports `--resume`/partial reports plus first-class chunk-summary validation, Lean/Lake toolchain preflight, and Lake cache-template recovery; see `docs/ERDOS_STRAUS_BOUNDED_STRESS.md`.\n\nThe van der Waerden lower-bound example is a third finite/bounded registry benchmark. It generates explicit two-coloring certificates for `3 ≤ n ≤ 8` with no monochromatic 3-term arithmetic progression and proves the public Lean theorem `van_der_waerden_two_color_three_term_lower_bound_eight`; see `docs/VAN_DER_WAERDEN_LOWER_BOUND_BOUNDED.md`.\n\nValidate the package and examples with:\n\n```bash\nnpm run validate\nnpm run typecheck\nnpm run validate:extension\nnpm run validate:schemas\nnpm run validate:artifacts\nnpm run validate:evidence\nnpm run validate:generated\nnpm run audit:benchmarks -- --dry-run\nnpm run audit:benchmarks -- --out-root /tmp/pi-autocontext-erdos-benchmark-audits\nnpm run smoke:installed\nnpm run validate:example\nnpm run validate:lake-example\n```\n\n## AutoContext-backed tool\n\nThe package registers one consolidated Pi tool:\n\n```text\nautocontext_erdos\n```\n\nActions:\n\n- `preflight`: check Lean and `uvx autoctx improve` availability.\n- `init_problem`: create the run artifact layout.\n- `verify_file`: run Lean on a formalization and write attempt artifacts.\n- `autocontext_improve`: invoke `autoctx improve` with a Lean verifier command and save prompt/rubric/logs/best candidate/verdict.\n- `export_fixed_template`: freeze a named theorem into a `Theorem.template.lean` fixture with a `{{PROOF}}` hole for `pi-autocontext-lean-verify` proof-body repair.\n- `audit_theorems`: final-artifact audit that verifies one or more Lean files, optionally runs `lake build <target>` first, runs `#print axioms`, checks forbidden constructs, compares per-file imports to optional baselines, and records environment/toolchain hashes.\n- `lemma_graph`: initialize, propose candidate lemmas, validate, summarize, advance, and record results for dependency graphs under `lemmas/lemma_graph.json`. The `propose` mode merges agent-generated candidate nodes as `planned`, skipping duplicates and recorded dead ends.\n- `generate_bounded_certificates`: generate or check bounded Erdős–Straus certificate runs with reproducible artifact hashes; Lean verification is still required for proof claims.\n- `validate_artifacts`: validate schema-stamped bounded certificate, artifact integrity, theorem-audit, and stress artifacts under a run root/audit root.\n- `summarize_run`: summarize files and attempt verdicts under a run root.\n\nThe standalone registry-driven audit runner reads `benchmarks/index.json` and invokes the same Lean/Lake audit stages for every registered benchmark. Use `--list` or `--dry-run` to inspect the plan before running Lean/Lake:\n\n```bash\nnode scripts/audit-benchmarks.mjs --list\nnode scripts/audit-benchmarks.mjs --dry-run\nELAN_HOME=/tmp/autocontext-elan-home \\\nLEAN_BIN=/tmp/autocontext-elan-home/bin/lean \\\nnode scripts/audit-benchmarks.mjs --out-root /tmp/pi-autocontext-erdos-benchmark-audits\n```\n\nRelease evidence can be cross-checked against npm, git tags, and GitHub Actions runs:\n\n```bash\nnode scripts/validate-evidence.mjs --file docs/release-evidence/<version>.json --cross-check\n```\n\nThe AutoContext action uses direct Lean verification by default:\n\n```text\nuvx --python 3.12 --from autocontext==0.5.1 autoctx improve ... --verify-cmd \"<lean> {file}\"\n```\n\nFor Mathlib or local Lake-project imports, pass `verificationMode=\"lake\"` and `projectRoot`; verification and AutoContext rechecks then use `lake env lean <file>`. Multi-module generated examples such as the chunked Erdős–Straus certificate benchmark are built with `lake build Formalization` before root/candidate rechecks. For final audits, pass `lakeBuildTarget=\"Formalization\"` plus `auditFiles` to capture the Lake build, per-module Lean verification, per-module import baselines, and per-theorem axiom results in one audit root. `init_problem` can scaffold a Mathlib-aware Lake project with `withMathlib=true`. See `docs/LAKE_MATHLIB_SUPPORT.md` and `docs/THEOREM_AUDIT.md`.\n\nFor whole-file repair, pass `preserveTheorems` to require exact normalized theorem-statement preservation before a Lean-verified candidate is accepted:\n\n```json\n{\n  \"action\": \"autocontext_improve\",\n  \"preserveTheorems\": [\"mod_three_eq_zero_or_one_or_two\", \"egz_three_nat\"]\n}\n```\n\nIf Lean accepts a candidate but a preserved theorem statement changes, the verdict is `theorem_statement_changed` with `Accepted: false`.\n\nFor the compact EGZ `n = 3` repair loop, current validation recommends `timeoutSeconds=240`; `timeoutSeconds=120` is useful but budget-limited for this task.\n\nWhen a theorem statement is ready to freeze, use `export_fixed_template` to hand off proof-body-only repair to `pi-autocontext-lean-verify`; see `docs/LEAN_VERIFY_HANDOFF.md`.\n\nBefore treating a final theorem as a serious result, run `audit_theorems`; see `docs/THEOREM_AUDIT.md`.\n\n## MVP workflow\n\nA typical run creates a durable folder such as:\n\n```text\nruns/<problem-slug>/\n  problem.md\n  source_notes.md\n  formalization/\n    Formalization.lean\n    formalization_notes.md\n  lemmas/\n    lemma_plan.md\n  attempts/\n    0001/\n      prompt.md\n      candidate.lean\n      lean.stderr.txt\n      verdict.md\n  reports/\n    final_report.md\n```\n\nEvery mathematical claim in the final report must be labeled as one of:\n\n- Lean verified;\n- formalization draft;\n- conjecture;\n- heuristic/proof sketch;\n- failed attempt.\n\n## Guardrail posture\n\nNever count a proof unless Lean verifies the exact theorem or unchanged template. Do not use `sorry`, `admit`, new axioms, `unsafe`, theorem weakening, proof-by-importing-answer, or hidden assumptions as success criteria.\n","readmeFilename":"README.md"}