Pith Number

pith:LUN66YRQ

pith:2013:LUN66YRQKQJYWXMWLYZXFXKQVI

not attested not anchored not stored refs pending

Recurrence Relations for Graph Polynomials on Bi-iterative Families of Graphs

Johann A. Makowsky, Tomer Kotek

arxiv:1309.4020 v1 · 2013-09-16 · 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{LUN66YRQKQJYWXMWLYZXFXKQVI}

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	2026-05-18T03:13:11.476134Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5d1bef623054138b5d965e3372dd50aa382b924bbe46685ee6bf50930b6b01d9

Aliases

arxiv: 1309.4020 · arxiv_version: 1309.4020v1 · doi: 10.48550/arxiv.1309.4020 · pith_short_12: LUN66YRQKQJY · pith_short_16: LUN66YRQKQJYWXMW · pith_short_8: LUN66YRQ

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/LUN66YRQKQJYWXMWLYZXFXKQVI \
  | 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: 5d1bef623054138b5d965e3372dd50aa382b924bbe46685ee6bf50930b6b01d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8162e33277a2f6769ec42835418f5cd012024dc46d9cf66075b0ec42a8bb431",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-09-16T16:13:41Z",
    "title_canon_sha256": "a22cf52e6d357cf581256d78d32073c30d07754ddcdbc3e352da3c157ae7b802"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.4020",
    "kind": "arxiv",
    "version": 1
  }
}