Pith Number

pith:ZBOE6ZPJ

pith:2025:ZBOE6ZPJSNV3LXZ6I4PV3JX6LL

not attested not anchored not stored refs pending

Frobenius theorem and fine structure of tangency sets to non-involutive distributions

Andrea Merlo, Annalisa Massaccesi, Giovanni Alberti

arxiv:2506.03715 v1 · 2025-06-04 · math.DG · math.AP · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZBOE6ZPJSNV3LXZ6I4PV3JX6LL}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-05T11:15:50.440354Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c85c4f65e9936bb5df3e471f5da6fe5ad78112a5af3ef68328dad2cdbd7b9a7d

Aliases

arxiv: 2506.03715 · arxiv_version: 2506.03715v1 · doi: 10.48550/arxiv.2506.03715 · pith_short_12: ZBOE6ZPJSNV3 · pith_short_16: ZBOE6ZPJSNV3LXZ6 · pith_short_8: ZBOE6ZPJ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZBOE6ZPJSNV3LXZ6I4PV3JX6LL \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c85c4f65e9936bb5df3e471f5da6fe5ad78112a5af3ef68328dad2cdbd7b9a7d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0edac4fe2d15f8cde973d2271ea8a79530c3fa987bf4a1be9037fb79e3574a2e",
    "cross_cats_sorted": [
      "math.AP",
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-06-04T08:46:32Z",
    "title_canon_sha256": "2c9e6a26f89f78ccf26f2ce40756c3e315c63e4ca9217adf55fa92451c918e17"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.03715",
    "kind": "arxiv",
    "version": 1
  }
}