docs/REPRODUCING.md

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

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:

   cd lean
   lake update
   lake exe cache get
   lake build
   lake exe meso-extractor-tests
   

2. Export the Mathlib corpus:

   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:

   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:

   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:

   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:

   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.