Pith Number

pith:L2G6CSX5

pith:2010:L2G6CSX5E4T565UAS7IDCIZKEA

not attested not anchored not stored refs pending

A Generalization of the Turaev Cobracket and the Minimal Self-Intersection Number of a Curve on a Surface

Patricia Cahn

arxiv:1004.0532 v3 · 2010-04-04 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L2G6CSX5E4T565UAS7IDCIZKEA}

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	2026-05-18T04:34:46.104368Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e8de14afd2727df768097d031232a20235d0afbe5bbf04a22377d9a1104d566

Aliases

arxiv: 1004.0532 · arxiv_version: 1004.0532v3 · doi: 10.48550/arxiv.1004.0532 · pith_short_12: L2G6CSX5E4T5 · pith_short_16: L2G6CSX5E4T565UA · pith_short_8: L2G6CSX5

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/L2G6CSX5E4T565UAS7IDCIZKEA \
  | 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: 5e8de14afd2727df768097d031232a20235d0afbe5bbf04a22377d9a1104d566

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e09deb9608a2ed548e4ec851d252514ac5fe81e2c17358cd328f91dd6d5cb78f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-04-04T20:43:52Z",
    "title_canon_sha256": "9ebdc0e9a978cf587261b09947ac2044491488670264a19027f650c0962fa5b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.0532",
    "kind": "arxiv",
    "version": 3
  }
}