Pith Number

pith:P7OLSAWO

pith:2012:P7OLSAWODQ5PMYNGY7H63Y6N3B

not attested not anchored not stored refs pending

Simplified numerical form of universal finite type invariant of Gauss words

Takaaki Yamanoi, Takayuki Yamaguchi, Tomonori Fukunaga

arxiv:1209.0287 v1 · 2012-09-03 · 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{P7OLSAWODQ5PMYNGY7H63Y6N3B}

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	2026-05-18T03:00:49.836721Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7fdcb902ce1c3af661a6c7cfede3cdd8671b288db410ac01edbd593e97b06631

Aliases

arxiv: 1209.0287 · arxiv_version: 1209.0287v1 · doi: 10.48550/arxiv.1209.0287 · pith_short_12: P7OLSAWODQ5P · pith_short_16: P7OLSAWODQ5PMYNG · pith_short_8: P7OLSAWO

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/P7OLSAWODQ5PMYNGY7H63Y6N3B \
  | 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: 7fdcb902ce1c3af661a6c7cfede3cdd8671b288db410ac01edbd593e97b06631

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a88f6c387d1121b00e3a6e07397dbb36218934cf742d450368fe30323acafd8",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-09-03T10:02:52Z",
    "title_canon_sha256": "0e7710c5c9d30e465a22d31dd0949c393257056f59fac628fca7f3219e5489e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0287",
    "kind": "arxiv",
    "version": 1
  }
}