| --- |
| 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`. |
|
|
|
|
