Pith Number

pith:ZBNJ5DFK

pith:2019:ZBNJ5DFKSWPX7L4SSHYUHHV7LZ

not attested not anchored not stored refs pending

On the integrability of the Abel and of the extended Li\'{e}nard equations

Man Kwong Mak, Tiberiu Harko

arxiv:1908.03730 v1 · 2019-08-10 · math.CA · math-ph · math.MP · nlin.SI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZBNJ5DFKSWPX7L4SSHYUHHV7LZ}

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	2026-07-05T01:03:19.919308Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c85a9e8caa959f7faf9291f1439ebf5e75e227220f3a189926d97e288799a484

Aliases

arxiv: 1908.03730 · arxiv_version: 1908.03730v1 · doi: 10.48550/arxiv.1908.03730 · pith_short_12: ZBNJ5DFKSWPX · pith_short_16: ZBNJ5DFKSWPX7L4S · pith_short_8: ZBNJ5DFK

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/ZBNJ5DFKSWPX7L4SSHYUHHV7LZ \
  | 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: c85a9e8caa959f7faf9291f1439ebf5e75e227220f3a189926d97e288799a484

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b072d21428fd2764561ee68e0a51da572f1fdf8ab7c7674cfb7afbf0fb96bd80",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "nlin.SI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2019-08-10T11:00:22Z",
    "title_canon_sha256": "bfab0954848fa2ca48fec34960531f19b80859c5a80b915a7ec5a409a43c5a85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.03730",
    "kind": "arxiv",
    "version": 1
  }
}