[{"data":1,"prerenderedAt":4},["ShallowReactive",2],{"qpG8PrQXwQ":3},"# MIPStarRE\n\n[![PR CI](https://github.com/LionSR/MIPStarRE/actions/workflows/pr-ci.yml/badge.svg)](https://github.com/LionSR/MIPStarRE/actions/workflows/pr-ci.yml)\n[![Compile blueprint](https://github.com/LionSR/MIPStarRE/actions/workflows/blueprint.yml/badge.svg)](https://github.com/LionSR/MIPStarRE/actions/workflows/blueprint.yml)\n![sorries](https://img.shields.io/endpoint?url=https://sirui-lu.com/MIPStarRE/badges/sorries.json)\n![axioms](https://img.shields.io/endpoint?url=https://sirui-lu.com/MIPStarRE/badges/axioms.json)\n![Lean](https://img.shields.io/endpoint?url=https://sirui-lu.com/MIPStarRE/badges/lean.json)\n![Mathlib](https://img.shields.io/endpoint?url=https://sirui-lu.com/MIPStarRE/badges/mathlib.json)\n![blueprint: no \\leanok](https://img.shields.io/endpoint?url=https://sirui-lu.com/MIPStarRE/badges/blueprint_no_leanok.json)\n![blueprint: not ready](https://img.shields.io/endpoint?url=https://sirui-lu.com/MIPStarRE/badges/blueprint_not_ready.json)\n\n\u003Cp align=\"center\">\n  \u003Ca href=\"https://sirui-lu.com/MIPStarRE/blueprint/\">Blueprint\u003C/a> ·\n  \u003Ca href=\"https://sirui-lu.com/MIPStarRE/docs/\">Documentation\u003C/a> ·\n  \u003Ca href=\"https://sirui-lu.com/MIPStarRE/paper-gaps/\">Paper-gap notes\u003C/a>\n\u003C/p>\n\nFormalization project for mathematics around $\\mathrm{MIP}^*=\\mathrm{RE}$.\n\n## Active paper track\n\nThe current active proof-following track is:\n\n- arXiv:2009.12982, *Quantum soundness of the classical low individual degree test* (LDT).\n\nThe in-repo paper source mirror lives at `references/ldt-paper/`.\n\n## Source-of-truth order (LDT)\n\nWhen working on the active track, consult these locations in this order:\n\n1. **`references/ldt-paper/`** — in-repo TeX source mirror for the paper. This is the mathematical ground truth.\n2. **`blueprint/src/chapter/`** — active, dependency-tracked LaTeX blueprint with Lean cross-references (`\\lean{}`, `\\leanok`).\n3. **`MIPStarRE/`** — Lean scaffold that matches the blueprint. Declarations in `MIPStarRE.LDT.*` are cross-referenced from the blueprint.\n\nSupporting notes:\n\n- `audits/2026-03-20_ldt-source-map.md` — source-file / theorem-ownership map\n- `audits/2026-03-20_ldt-blueprint-dependency-review.md` — dated dependency-review snapshot (context, not canonical)\n\nThe blueprint is organized by **theorem ownership and proof dependency**, not by raw TeX input order.\n\n## Repository layout\n\n```\nMIPStarRE/\n├── Quantum/               # Reusable matrix / measurement infrastructure\n│   ├── FiniteHilbert.lean\n│   ├── FiniteMatrix.lean\n│   ├── Measurement.lean\n│   └── ProjectorONB.lean\n└── LDT/                   # Low individual degree test (12 submodules)\n    ├── Basic/             # Parameters, operators, distributions, submeasurements\n    ├── Test/              # Test definitions & main theorem\n    ├── Preliminaries/\n    ├── MakingMeasurementsProjective/\n    ├── MainInductionStep/\n    ├── ExpansionHypercubeGraph/\n    ├── GlobalVariance/\n    ├── SelfImprovement/\n    ├── CommutativityPoints/\n    ├── Commutativity/\n    ├── Pasting/\n    └── Tactic/            # Project-local tactics & simp sets\n```\n\nEach LDT submodule typically contains `Defs.lean` and `Theorems.lean` (larger\nsubmodules split these across subdirectories). The root module `MIPStarRE.lean`\nre-exports `MIPStarRE.Quantum` and `MIPStarRE.LDT`.\n\nTop-level directories:\n\n- `MIPStarRE/` — Lean source (see above)\n- `blueprint/src/` — active LDT blueprint (chapters under `blueprint/src/chapter/`)\n- `references/ldt-paper/` — in-repo TeX source for the LDT paper\n- `docs/` — contributor guides, style, naming, proof integrity, CI notes\n- `audits/` — dated chapter-by-chapter dependency-scouting reports\n\n## Recommended proof-filling order\n\nThe source-file order is not the proof-dependency order. The recommended implementation order is:\n\n1. Sections 3–4: test setup and preliminaries\n2. Section 5: making measurements projective\n3. Sections 7–8: expansion and global variance\n4. Section 9: self-improvement\n5. Sections 10–11: commutativity\n6. Section 12: pasting\n7. Section 6: main induction wrapper\n\n## Build\n\n**Toolchain**: See `lean-toolchain` and `lakefile.toml` for the pinned Lean and Mathlib versions.\n\nFrom the repo root:\n\n```bash\n# First-time setup: fetch the Mathlib cache, then build\nlake exe cache get\nlake build\n\n# Type-check a single file (fastest iteration loop)\nlake env lean MIPStarRE/LDT/SelfImprovement/Defs.lean\n\n# Check declarations referenced from the blueprint\nlake exe checkdecls blueprint/lean_decls\n```\n\nBlueprint commands (from the repo root, with `leanblueprint` on your `PATH`):\n\n```bash\nleanblueprint pdf    # PDF output\nleanblueprint web    # HTML output\n```\n\n## Contributing\n\nStart with [`docs/CONTRIBUTING.md`](docs/CONTRIBUTING.md) for PR/issue conventions and the review checklist. Key references:\n\nShared Mathlib-style conventions (style, naming, documentation, PR review,\nproof integrity, prose) live in the `lean-conventions` skill of\n[texra-ai/texra-lean-skills](https://github.com/texra-ai/texra-lean-skills),\nauto-installed for Claude Code via `.claude/settings.json` (other agents:\nclone the repository and symlink the skill directories into the agent's\nskill location, as described in its README).\n\nMIPStarRE-local references:\n\n| File | Purpose |\n|------|---------|\n| `docs/CONTRIBUTING.md` | PR format, issue templates, label taxonomy, review checklist |\n| `docs/project_conventions.md` | MIPStarRE-local addenda to the shared conventions (linter warnings, source-faithfulness review, proof integrity) |\n| `docs/mathematical_language.md` | Project-local mathematical language rules for Lean names and documentation |\n| `docs/blueprint_style_guide.md` | Blueprint notation and section conventions |\n| `docs/ci-automation.md` | CI/CD workflow details |\n| `audits/` | Chapter-by-chapter Mathlib dependency scouting reports |\n\nWhen adding or completing a declaration, update the corresponding blueprint entry in `blueprint/src/chapter/`: add `\\lean{DeclName}` and `\\leanok` for new results, or `\\leanok` on `\\begin{proof}` for newly proven results.\n",1792957682365]