Pith Number

pith:2GKAJ7R6

pith:2010:2GKAJ7R6Q3RZ6WMYFAMI7QYP5R

not attested not anchored not stored refs pending

A geometric approach to integrability of Abel differential equations

Javier de Lucas, Jos\'e F. Cari\~nena, Manuel F. Ra\~nada

arxiv:1012.2257 v1 · 2010-12-10 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2GKAJ7R6Q3RZ6WMYFAMI7QYP5R}

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	2026-05-18T04:18:23.369502Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d19404fe3e86e39f599828188fc30fec6734f25a2b2eea32c0a38b4464dba144

Aliases

arxiv: 1012.2257 · arxiv_version: 1012.2257v1 · doi: 10.48550/arxiv.1012.2257 · pith_short_12: 2GKAJ7R6Q3RZ · pith_short_16: 2GKAJ7R6Q3RZ6WMY · pith_short_8: 2GKAJ7R6

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/2GKAJ7R6Q3RZ6WMYFAMI7QYP5R \
  | 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: d19404fe3e86e39f599828188fc30fec6734f25a2b2eea32c0a38b4464dba144

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43a5579ee37ea6ba9fabf7c3e39bf6d56f7ece40c94206c492679c69dea18a41",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-12-10T13:16:09Z",
    "title_canon_sha256": "5a0415df7c341f66ef5ced7f1fd29666c0babd672f29383508f1a6fa7fbd6c3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2257",
    "kind": "arxiv",
    "version": 1
  }
}