# 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.