Pith Number

pith:YZZPJ3XY

pith:2011:YZZPJ3XYK2YEYCPYPNMXOLWRPY

not attested not anchored not stored refs pending

Kei modules and unoriented link invariants

Mike Grier, Sam Nelson

arxiv:1102.4366 v1 · 2011-02-21 · math.GT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YZZPJ3XYK2YEYCPYPNMXOLWRPY}

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	2026-05-18T04:28:09.139171Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c672f4eef856b04c09f87b59772ed17e0e0c39ccdae5c48b0bf270feee6499cf

Aliases

arxiv: 1102.4366 · arxiv_version: 1102.4366v1 · doi: 10.48550/arxiv.1102.4366 · pith_short_12: YZZPJ3XYK2YE · pith_short_16: YZZPJ3XYK2YEYCPY · pith_short_8: YZZPJ3XY

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/YZZPJ3XYK2YEYCPYPNMXOLWRPY \
  | 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: c672f4eef856b04c09f87b59772ed17e0e0c39ccdae5c48b0bf270feee6499cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b9e43edf7cb9d33ac0a736ef868c8a0afa5069e09b70614d370819957583ee2",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-02-21T23:19:10Z",
    "title_canon_sha256": "42ec3af9e18bfa9530124d0e2385d57e6552a15fb93335d6878e02ef5b7b967d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.4366",
    "kind": "arxiv",
    "version": 1
  }
}