Pith Number

pith:EXKOA5GT

pith:2010:EXKOA5GTU473IBLFTS435WSFNY

not attested not anchored not stored refs pending

The incidence Hopf algebra of graphs

Brandon Humpert, Jeremy L. Martin

arxiv:1012.4786 v3 · 2010-12-21 · math.CO · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EXKOA5GTU473IBLFTS435WSFNY}

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	2026-05-18T04:00:28.509688Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

25d4e074d3a73fb405659cb9beda456e183de9a89c9253950e6a6a7097838599

Aliases

arxiv: 1012.4786 · arxiv_version: 1012.4786v3 · doi: 10.48550/arxiv.1012.4786 · pith_short_12: EXKOA5GTU473 · pith_short_16: EXKOA5GTU473IBLF · pith_short_8: EXKOA5GT

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/EXKOA5GTU473IBLFTS435WSFNY \
  | 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: 25d4e074d3a73fb405659cb9beda456e183de9a89c9253950e6a6a7097838599

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d97f24edac9e914117d0f6af36fef97cc97c22615fba1004ec969bacf19e1951",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-12-21T20:38:58Z",
    "title_canon_sha256": "4e33464fc5b08d0abf3047ce2f4e130a84789f643c66f756cf56a7bd484a502e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4786",
    "kind": "arxiv",
    "version": 3
  }
}