Pith Number

pith:KBRCAUQ7

pith:2012:KBRCAUQ7LZ6YIXJKSIHR6CCWPA

not attested not anchored not stored refs pending

A generalization of Vassiliev's planarity criterion

Tyler Friesen

arxiv:1210.1539 v1 · 2012-10-04 · math.CO · 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{KBRCAUQ7LZ6YIXJKSIHR6CCWPA}

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	2026-05-18T03:44:03.182056Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

506220521f5e7d845d2a920f1f08567827a0a2bf87917ce8d7025564a360cf2d

Aliases

arxiv: 1210.1539 · arxiv_version: 1210.1539v1 · doi: 10.48550/arxiv.1210.1539 · pith_short_12: KBRCAUQ7LZ6Y · pith_short_16: KBRCAUQ7LZ6YIXJK · pith_short_8: KBRCAUQ7

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/KBRCAUQ7LZ6YIXJKSIHR6CCWPA \
  | 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: 506220521f5e7d845d2a920f1f08567827a0a2bf87917ce8d7025564a360cf2d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e02f9123f22cf28a131fbdf6c5aa5cb2b577376585c8b16dfbc93075a1d1175b",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-10-04T18:55:32Z",
    "title_canon_sha256": "590196833721b2c82a378f2b4d3dc0f96eeb180906d7299ef3c38e3fb01d6553"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.1539",
    "kind": "arxiv",
    "version": 1
  }
}