Pith Number

pith:52Q72CJR

pith:2011:52Q72CJR4O76CMLXOIQRWSA6P3

not attested not anchored not stored refs pending

The Geometry of Flex Tangents to a Cubic Curve and its Parameterizations

Jean-Gabriel Kammerer, Jean-Marc Couveignes

arxiv:1101.3630 v2 · 2011-01-19 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{52Q72CJR4O76CMLXOIQRWSA6P3}

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	2026-05-18T03:56:24.321832Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eea1fd0931e3bfe1317772211b481e7ef412e9880ccf8802e94e2418aa92028a

Aliases

arxiv: 1101.3630 · arxiv_version: 1101.3630v2 · doi: 10.48550/arxiv.1101.3630 · pith_short_12: 52Q72CJR4O76 · pith_short_16: 52Q72CJR4O76CMLX · pith_short_8: 52Q72CJR

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/52Q72CJR4O76CMLXOIQRWSA6P3 \
  | 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: eea1fd0931e3bfe1317772211b481e7ef412e9880ccf8802e94e2418aa92028a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "742b774915f2b3a22586a3e22e5aa0c987d868792a8afd84cf30cc2ab6ec54fd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-01-19T07:31:03Z",
    "title_canon_sha256": "c9e2928e621d6488fb88b6d5d1bf1b1b68280f7cdb44595a01dbe494f9c9a66d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.3630",
    "kind": "arxiv",
    "version": 2
  }
}