Pith Number

pith:ULR3PNS2

pith:2013:ULR3PNS25BFFYZOS3O24URH3ZI

not attested not anchored not stored refs pending

On a theorem of Lyapounov

Antonio Giorgilli

arxiv:1303.7322 v1 · 2013-03-29 · 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{ULR3PNS25BFFYZOS3O24URH3ZI}

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	2026-05-18T03:29:28.880451Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2e3b7b65ae84a5c65d2dbb5ca44fbca33c9294ca068399a407f3f49ede9ec1d

Aliases

arxiv: 1303.7322 · arxiv_version: 1303.7322v1 · doi: 10.48550/arxiv.1303.7322 · pith_short_12: ULR3PNS25BFF · pith_short_16: ULR3PNS25BFFYZOS · pith_short_8: ULR3PNS2

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/ULR3PNS25BFFYZOS3O24URH3ZI \
  | 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: a2e3b7b65ae84a5c65d2dbb5ca44fbca33c9294ca068399a407f3f49ede9ec1d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77ece593226c5ead6d867c397ccb2b20a93746f0b775428bf95f6fd4f45bbc0e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-03-29T08:18:45Z",
    "title_canon_sha256": "6c7dac69a6c4eef17e43c0c85b52e8fb6c2159a95d05510008a5618988d5d6a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.7322",
    "kind": "arxiv",
    "version": 1
  }
}