README.md

metadata

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 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:

• 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. 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:

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.