Pith Number

pith:4P4PR3PC

pith:2011:4P4PR3PCSDVVJUIH2A5I4MGL4A

not attested not anchored not stored refs pending

Homomorphic expansions for knotted trivalent graphs

Dror Bar-Natan, Zsuzsanna Dancso

arxiv:1103.1896 v4 · 2011-03-09 · math.QA · 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{4P4PR3PCSDVVJUIH2A5I4MGL4A}

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	2026-05-18T03:49:58.574597Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3f8f8ede290eb54d107d03a8e30cbe02d1bce27f4d6e2cf69484e5610134249

Aliases

arxiv: 1103.1896 · arxiv_version: 1103.1896v4 · doi: 10.48550/arxiv.1103.1896 · pith_short_12: 4P4PR3PCSDVV · pith_short_16: 4P4PR3PCSDVVJUIH · pith_short_8: 4P4PR3PC

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/4P4PR3PCSDVVJUIH2A5I4MGL4A \
  | 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: e3f8f8ede290eb54d107d03a8e30cbe02d1bce27f4d6e2cf69484e5610134249

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "52cfae4e3ed4eb60011399f03a53744dc47f5228248612adfa43f1dae033d833",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2011-03-09T21:41:41Z",
    "title_canon_sha256": "dd5c830e5e228c299b2dc23becb9343e4f0ceff0701fad5f3bbd060d0eb572f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.1896",
    "kind": "arxiv",
    "version": 4
  }
}