---
pretty_name: MesoMathematics — Mathlib 4.33 proof-network artifacts
license: apache-2.0
language:
- en
tags:
- lean
- mathlib
- theorem-proving
- formal-mathematics
- hypergraph
- network-science
configs:
- config_name: mathlib-declarations-v4.33.0
  data_files:
  - split: train
    path: raw/mathlib-v4.33.0/declarations-*.jsonl
---

# MesoMathematics

Frozen data artifacts for the paper **“Mathematical Knowledge at the
Mesoscale: Organization after the Formal Mathematics Revolution”** by Andrea
E. V. Ferrari, Benjy Firester, Xinze Li, Simone Severini, and Patrick Shafto.
The corresponding source code, exact commands, and manuscript live in the
[`MathNetwork/MesoMathematics`](https://github.com/MathNetwork/MesoMathematics)
repository.

This release fixes Mathlib at `v4.33.0`, commit
`db584cd6d46c92f209a44c0f1c829460d327499d`, with Lean `v4.33.0`.  The full
commit, not the tag, identifies the corpus.  It also records the Section 3.4
comparison against `metamath/set.mm` commit
`057f4c461055d0b1ed78d9d333aa3de34d9771fa`.

## What is here

| path | contents |
|---|---|
| `raw/mathlib-v4.33.0/` | 569,189 Lean declarations in 57 JSONL shards, plus the extractor manifest |
| `derived/mathlib-v4.33.0/primary-theorem-hypergraph.json` | primary theorem view: 251,416 vertices and 195,884 retained-proof hyperedges |
| `derived/mathlib-v4.33.0/sensitivity-internal-only-theorem-hypergraph.json` | legacy-filter sensitivity view: 276,024 vertices and 200,602 hyperedges |
| `results/` | claim-addressed outputs for Sections 3 and 4, including sensitivity results |
| `labels/` | the reviewed 36-declaration Ahlfors target and its native Lean audit |
| `spec/` | normative definitions of the corpus, statistics, and navigation experiment |
| `verification/` | independent Metamath-adapter cross-check |
| `metadata/claims.json` | paper-section-to-artifact registry |
| `metadata/release.json` | frozen source revisions, counts, sizes, and release identity |
| `SHA256SUMS` | SHA-256 digest for every published file except the checksum file itself |

The raw declaration rows have the schema `mesomath-corpus-v2`.  Each row
records its Lean name, defining module and namespace, declaration kind,
reducibility, references appearing in its elaborated type and stored value,
sharing-aware DAG sizes, definition height, and auto/private/internal-name
flags.  Referenced declarations are not unfolded.

The two hypergraph files have schema `mesomath-theorem-hypergraph-v2`.
`vertices` stores a stable integer ID and theorem metadata.  An entry
`{"inputs": [...], "output": i}` in `edges` represents the set of retained
theorem premises consumed by the stored proof of vertex `i`.  Each theorem has
one stored Lean proof; consequently every depth, reuse, and compression
measurement is relative to that retained proof.

## Which object supports which claim

The authoritative map is [`metadata/claims.json`](metadata/claims.json):

- `S3.1-depth-growth.json`: recorded depth and pairwise-closure controls;
- `S3.2-namespace-depth.json`: namespace-level depth summaries;
- `S3.3-compression-reuse.json`: compression–reuse association and bootstrap interval;
- `S3.4-projection-geometry.json`: projection sensitivity, spectral dimension,
  four-point hyperbolicity, and degree-preserving null ensembles;
- `S3.4-metamath.json`: the pinned cross-library comparison;
- `S4.1-navigation.json`: the reviewed Mathlib 4.33 complex-analysis ranking pilot.

These files supersede the historical v4.30-era numerical artifacts.  They
must not be mixed with numbers from an earlier Mathlib snapshot.

## Reproduction and verification

Start with [`docs/REPRODUCING.md`](docs/REPRODUCING.md).  It separates the
native Lean export, graph-view materialization, statistical analyses,
Metamath adapter, and navigation experiment.  The source repository pins the
Lean toolchain and Python environment and contains the tests.  A complete
second Section 4 run produced a byte-identical output file.

To check this deposit after download:

```bash
shasum -a 256 -c SHA256SUMS
```

## Scope and limitations

This is a trace of one formal library, language, community, snapshot, and one
retained proof per theorem.  It is not a unique graph of mathematics.  The
declaration graph used in Section 4 is a parallel view of the same exported
corpus, not a projection of the theorem-only hypergraph.  Namespace regions
are reproducible library partitions, not claims about intrinsic disciplinary
boundaries.  Projection-dependent geometry is reported together with its
comparison model rather than as an invariant of the corpus.

## Licenses

Mathlib-derived exports and graph artifacts are distributed under the Apache
License 2.0; the upstream license text is included at
`licenses/mathlib-APACHE-2.0.txt`.  The source `set.mm` database is not
redistributed here: only aggregate comparison results are included.  Upstream
`set.mm` is dedicated to the public domain under CC0; its license text is
included at `licenses/set.mm-CC0.txt`.