Pith Number

pith:EFZQ7QYY

pith:2000:EFZQ7QYYHLWRMSTWPCKLCAAMA6

not attested not anchored not stored refs pending

Counting Paths in Graphs

Laurent Bartholdi

arxiv:math/0012161 v2 · 2000-12-18 · math.CO · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EFZQ7QYYHLWRMSTWPCKLCAAMA6}

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	2026-07-04T15:12:00.293748Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

21730fc3183aed164a767894b1000c0798cfab756ebd9ebc1fc7d209be5fe504

Aliases

arxiv: math/0012161 · arxiv_version: math/0012161v2 · doi: 10.48550/arxiv.math/0012161 · pith_short_12: EFZQ7QYYHLWR · pith_short_16: EFZQ7QYYHLWRMSTW · pith_short_8: EFZQ7QYY

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/EFZQ7QYYHLWRMSTWPCKLCAAMA6 \
  | 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: 21730fc3183aed164a767894b1000c0798cfab756ebd9ebc1fc7d209be5fe504

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8691afa7a5198191af333178770727c98743435393200317cb71d8fdd7b5c13",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2000-12-18T04:01:02Z",
    "title_canon_sha256": "091b646b9f842a41533d748c2db779dc414004313e4913a3d6062dcd48ca1ad4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0012161",
    "kind": "arxiv",
    "version": 2
  }
}