Pith Number

pith:37GRLOJ2

pith:2012:37GRLOJ2RRUNL32CZZEEAVPEZO

not attested not anchored not stored refs pending

A locally minimal, but not globally minimal bridge position of a knot

Kazuto Takao, Makoto Ozawa

arxiv:1203.1119 v3 · 2012-03-06 · 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{37GRLOJ2RRUNL32CZZEEAVPEZO}

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	2026-05-18T03:21:54.934881Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dfcd15b93a8c68d5ef42ce484055e4cb93b811e3f5b8708e9298c0ef2b07e6aa

Aliases

arxiv: 1203.1119 · arxiv_version: 1203.1119v3 · doi: 10.48550/arxiv.1203.1119 · pith_short_12: 37GRLOJ2RRUN · pith_short_16: 37GRLOJ2RRUNL32C · pith_short_8: 37GRLOJ2

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/37GRLOJ2RRUNL32CZZEEAVPEZO \
  | 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: dfcd15b93a8c68d5ef42ce484055e4cb93b811e3f5b8708e9298c0ef2b07e6aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac8fe3a47a8bfc1b8a3071dbf283f323db14489830f5784b56efb68eb4c795ed",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-03-06T07:35:31Z",
    "title_canon_sha256": "bf45f497aaeff1dd9c888ae2c0d48f38eb012bd7a7abdc39960e83ce1a1667d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.1119",
    "kind": "arxiv",
    "version": 3
  }
}