File size: 5,467 Bytes
e4dca97 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 | # 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.
|