Pith Number

pith:IH627PZV

pith:2004:IH627PZVEYT3H4DHEXPQVWMN3Q

not attested not anchored not stored refs pending

Non-backtracking random walks and cogrowth of graphs

Ronald Ortner, Wolfgang Woess

arxiv:math/0403414 v1 · 2004-03-24 · math.PR · 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{IH627PZVEYT3H4DHEXPQVWMN3Q}

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	2026-05-18T03:39:14.988594Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

41fdafbf352627b3f06725df0ad98ddc0551f7ee38b60234ea54c41937495940

Aliases

arxiv: math/0403414 · arxiv_version: math/0403414v1 · doi: 10.48550/arxiv.math/0403414 · pith_short_12: IH627PZVEYT3 · pith_short_16: IH627PZVEYT3H4DH · pith_short_8: IH627PZV

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/IH627PZVEYT3H4DHEXPQVWMN3Q \
  | 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: 41fdafbf352627b3f06725df0ad98ddc0551f7ee38b60234ea54c41937495940

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f495f06c1a3e5588ff09125471e15f47a7ba035e57ac3d68ab83ba58ef4ed24",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2004-03-24T15:24:18Z",
    "title_canon_sha256": "32ed9813f4f4c5a3979867eb5cb051c5e0264532e9f61292148b4d0056fa2303"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0403414",
    "kind": "arxiv",
    "version": 1
  }
}