Pith Number

pith:YYUN3XDF

pith:2011:YYUN3XDFWILHLXCVGSIXZV4RRS

not attested not anchored not stored refs pending

On a move reducing the genus of a knot diagram

Keiichi Sakai, Kenji Daikoku, Masamichi Takase

arxiv:1111.3215 v2 · 2011-11-14 · math.GT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YYUN3XDFWILHLXCVGSIXZV4RRS}

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	2026-05-18T03:20:58.944082Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c628dddc65b21675dc5534917cd7918c8baffa72ea4cc6305972acbf14337169

Aliases

arxiv: 1111.3215 · arxiv_version: 1111.3215v2 · doi: 10.48550/arxiv.1111.3215 · pith_short_12: YYUN3XDFWILH · pith_short_16: YYUN3XDFWILHLXCV · pith_short_8: YYUN3XDF

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/YYUN3XDFWILHLXCVGSIXZV4RRS \
  | 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: c628dddc65b21675dc5534917cd7918c8baffa72ea4cc6305972acbf14337169

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7aa8267fe1bf5780a2e44a1b6b4d41ec16cc32b98073d24ccd14a8c4643c7619",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-11-14T13:50:50Z",
    "title_canon_sha256": "5f156e8fdcf8548d9ff5d329e3a6b6778809a7782339eec9ee2c2cc63624b2ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.3215",
    "kind": "arxiv",
    "version": 2
  }
}