| # Reproducibility package |
|
|
| This directory reproduces the empirical claims in Sections 3 and 4 of the |
| paper. It is intentionally separate from `../paper`: the paper is a readable |
| article, while this directory fixes executable objects, parameters and result |
| artifacts. |
|
|
| ## Frozen corpus |
|
|
| | component | value | |
| |---|---| |
| | Mathlib release | `v4.33.0` | |
| | Mathlib commit | `db584cd6d46c92f209a44c0f1c829460d327499d` | |
| | Lean toolchain | `leanprover/lean4:v4.33.0` | |
| | Raw schema | `mesomath-corpus-v2` | |
| | set.mm commit | `057f4c461055d0b1ed78d9d333aa3de34d9771fa` | |
|
|
| The tag is descriptive; the full commit is authoritative. |
|
|
| ## Paper claims and experiment IDs |
|
|
| | ID | Paper claim | Inputs | Result artifact | |
| |---|---|---|---| |
| | `S3.1-depth-growth` | theorem graph is deep and sparse | primary theorem view | `results/S3.1-depth-growth.json` | |
| | `S3.2-namespace-depth` | namespace depths differ by over an order of magnitude | primary theorem view | `results/S3.2-namespace-depth.json` | |
| | `S3.3-compression-reuse` | proof-term/statement ratio is associated with reuse | primary theorem view | `results/S3.3-compression-reuse.json` | |
| | `S3.4-projection-geometry` | measurements depend on projection, but detected geometry lies within degree-preserving nulls | primary theorem hypergraph | `results/S3.4-projection-geometry.json` | |
| | `S3.4-metamath` | depth growth is similar across libraries but compression--reuse is not | Mathlib primary view and pinned `set.mm` | `results/S3.4-metamath.json` | |
| | `S4.1-navigation` | structure ranks a reviewed target above random | v4.33 declaration view and reviewed labels | `results/S4.1-navigation.json` | |
|
|
| `claims.json` is the machine-readable version of this table. A result is not |
| ready to enter the paper until it records the corpus manifest hash, analysis |
| configuration and random seed where relevant. Sections 3 and 4 have been |
| rerun on v4.33.0. Section 4's exact historical inputs remain as a regression |
| fixture, while the paper result uses the reviewed current statements and a |
| graph built entirely from the pinned v4.33.0 export. |
|
|
| ## Layout |
|
|
| ```text |
| experiments/ |
| claims.json claim-to-artifact registry |
| spec/ exact mathematical and computational objects |
| LEGACY_AUDIT.md claim-by-claim audit of the old implementation |
| legacy/ small immutable regression fixtures from old runs |
| lean/ native Mathlib environment extractor |
| analysis/ statistical analysis and figure generation |
| labels/ reviewed external labels (for Section 4) |
| data/raw/ Lean exports; generated, not committed |
| data/derived/ declared graph views; generated, not committed |
| results/ reviewed machine-readable result manifests |
| ``` |
|
|
| ## Reproduction stages |
|
|
| 1. Build and test the native extractor: |
|
|
| ```sh |
| cd lean |
| lake update |
| lake exe cache get |
| lake build |
| lake exe meso-extractor-tests |
| ``` |
|
|
| 2. Export the Mathlib corpus: |
|
|
| ```sh |
| lake exe meso-extract --out ../data/raw/mathlib-v4.33.0 |
| ``` |
|
|
| A fast format smoke test may import one module explicitly; this is never a |
| substitute for the full command above: |
|
|
| ```sh |
| lake exe meso-extract \ |
| --out /tmp/mesomath-smoke \ |
| --import-module Mathlib.Data.Nat.ModEq \ |
| --module-prefix Mathlib.Data.Nat.ModEq \ |
| --limit 25 |
| ``` |
|
|
| 3. Materialize the paper's graph views and run analyses: |
|
|
| ```sh |
| cd ../analysis |
| uv run pytest |
| uv run mesomath-analysis views \ |
| ../data/raw/mathlib-v4.33.0 ../data/derived/mathlib-v4.33.0 |
| uv run mesomath-analysis run-s3 \ |
| ../data/derived/mathlib-v4.33.0/primary-theorem-hypergraph.json \ |
| ../results |
| uv run mesomath-analysis run-geometry \ |
| ../data/derived/mathlib-v4.33.0/primary-theorem-hypergraph.json \ |
| ../results/S3.4-projection-geometry.json |
| ``` |
|
|
| The `views` command writes both the primary auto/private-filtered theorem |
| hypergraph and an internal-name-only sensitivity view matching the legacy |
| filter. Section 3 commands use the primary file unless explicitly pointed |
| at the sensitivity file. |
|
|
| 4. Clone the exact Metamath Proof Explorer snapshot and run the independent |
| cross-library adapter: |
|
|
| ```sh |
| git clone https://github.com/metamath/set.mm ../data/raw/set.mm |
| git -C ../data/raw/set.mm checkout 057f4c461055d0b1ed78d9d333aa3de34d9771fa |
| uv run mesomath-analysis run-metamath \ |
| ../data/raw/set.mm ../results/S3.4-metamath.json \ |
| --revision 057f4c461055d0b1ed78d9d333aa3de34d9771fa \ |
| --mathlib-depth-result ../results/S3.1-depth-growth.json \ |
| --mathlib-compression-result ../results/S3.3-compression-reuse.json |
| ``` |
|
|
| The parser's theorem count and selected reuse/proof-size values were |
| cross-checked against the official C verifier; the exact audit is recorded |
| in `verification/metamath-official-verifier.md`. |
|
|
| 5. Run the reviewed v4.33 declaration-graph experiment: |
|
|
| ```sh |
| uv run mesomath-analysis run-navigation \ |
| ../data/raw/mathlib-v4.33.0 \ |
| ../labels/ahlfors_positive_declarations_v4.33-review.csv \ |
| ../results/S4.1-navigation.json |
| ``` |
|
|
| A complete second run produced a byte-identical result file (SHA-256 |
| `76c7510f933daa39b0ae2ba42bd8e1d1728c481948bf03811a4e40aed4a2e9f3`). |
|
|
| The full-corpus commands are deliberately separate from unit tests: importing |
| and traversing all of Mathlib is an experiment run, not a build step. |
|
|
