Pith Number

pith:SNBQSIZL

pith:2003:SNBQSIZLR4KZD4WILEN6HD7MDH

not attested not anchored not stored refs pending

Amenability via random walks

Balint Virag, Laurent Bartholdi

arxiv:math/0305262 v1 · 2003-05-19 · math.GR · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SNBQSIZLR4KZD4WILEN6HD7MDH}

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	2026-05-18T04:08:43.049979Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

934309232b8f1591f2c8591be38fec19f5dfe7501cf5fe58acb14ddfde3894ad

Aliases

arxiv: math/0305262 · arxiv_version: math/0305262v1 · doi: 10.48550/arxiv.math/0305262 · pith_short_12: SNBQSIZLR4KZ · pith_short_16: SNBQSIZLR4KZD4WI · pith_short_8: SNBQSIZL

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/SNBQSIZLR4KZD4WILEN6HD7MDH \
  | 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: 934309232b8f1591f2c8591be38fec19f5dfe7501cf5fe58acb14ddfde3894ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a3774faf89062dd65fe48a03a4273b20e27d26aada00f0165bf1ca136ff034c8",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2003-05-19T06:03:57Z",
    "title_canon_sha256": "ea8abdf212ce39d3479740823aeebbe07ccc95b20634e8ab4868163c0219782a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0305262",
    "kind": "arxiv",
    "version": 1
  }
}