Pith Number

pith:4BOV7W6F

pith:2010:4BOV7W6FYYNHYDRCJK4CJLCLGP

not attested not anchored not stored refs pending

Polynomial invariants of graphs on surfaces

C. Estill, J. Michel, P. Stollenwerk, R. Askanazi, S. Chmutov

arxiv:1012.5053 v2 · 2010-12-22 · 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{4BOV7W6FYYNHYDRCJK4CJLCLGP}

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	2026-05-18T02:23:06.554678Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e05d5fdbc5c61a7c0e224ab824ac4b33f38877fef28f93465e73998bac7e9e65

Aliases

arxiv: 1012.5053 · arxiv_version: 1012.5053v2 · doi: 10.48550/arxiv.1012.5053 · pith_short_12: 4BOV7W6FYYNH · pith_short_16: 4BOV7W6FYYNHYDRC · pith_short_8: 4BOV7W6F

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/4BOV7W6FYYNHYDRCJK4CJLCLGP \
  | 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: e05d5fdbc5c61a7c0e224ab824ac4b33f38877fef28f93465e73998bac7e9e65

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3152d7e3f20b7b52eedf67948ebd82ba9526484bcd481aa5d9681512cad7e439",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-12-22T17:50:26Z",
    "title_canon_sha256": "b138f30f716c993102abc6fd5f1c3ea842b2427957505a06c18f5c9554f01be0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.5053",
    "kind": "arxiv",
    "version": 2
  }
}