Pith Number

pith:W3IJST42

pith:2010:W3IJST42CBZBC5TYQQ3ZJB5JTF

not attested not anchored not stored refs pending

Green bundles, Lyapunov exponents and regularity along the supports of the minimizing measures

Marie-Claude Arnaud

arxiv:1003.2139 v3 · 2010-03-10 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W3IJST42CBZBC5TYQQ3ZJB5JTF}

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	2026-05-18T04:02:37.881712Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6d0994f9a107211767884379487a99941bca678117fd4994625f778ba498596

Aliases

arxiv: 1003.2139 · arxiv_version: 1003.2139v3 · doi: 10.48550/arxiv.1003.2139 · pith_short_12: W3IJST42CBZB · pith_short_16: W3IJST42CBZBC5TY · pith_short_8: W3IJST42

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/W3IJST42CBZBC5TYQQ3ZJB5JTF \
  | 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: b6d0994f9a107211767884379487a99941bca678117fd4994625f778ba498596

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66946259144570b16872cfc3a5aaf7f0351358fcb2f6fac90ff290201821947e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-03-10T16:05:53Z",
    "title_canon_sha256": "524ab164944ecdcdfaebf07039ebc107899b9349ae7da1327fcea69f44add8d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.2139",
    "kind": "arxiv",
    "version": 3
  }
}