Pith Number

pith:UPDBKOED

pith:2002:UPDBKOEDE6K3WOPZ6CWOJC344N

not attested not anchored not stored refs pending

Dimension and randomness in groups acting on rooted trees

Balint Virag, Miklos Abert

arxiv:math/0212191 v2 · 2002-12-13 · 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{UPDBKOEDE6K3WOPZ6CWOJC344N}

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	2026-05-18T04:08:43.131513Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3c61538832795bb39f9f0ace48b7ce34b579296cc6d4b7d985e9a331c2b0a71

Aliases

arxiv: math/0212191 · arxiv_version: math/0212191v2 · doi: 10.48550/arxiv.math/0212191 · pith_short_12: UPDBKOEDE6K3 · pith_short_16: UPDBKOEDE6K3WOPZ · pith_short_8: UPDBKOED

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/UPDBKOEDE6K3WOPZ6CWOJC344N \
  | 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: a3c61538832795bb39f9f0ace48b7ce34b579296cc6d4b7d985e9a331c2b0a71

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8325f4ba7387fa48f28062d317ac9b46d0f39e22ebb8548ded618a2465a9c74",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2002-12-13T21:16:43Z",
    "title_canon_sha256": "7152bff90feeddfb804c26c7c9cc4ff41d4c08d4931f3877ffdfa3400e0b7aff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0212191",
    "kind": "arxiv",
    "version": 2
  }
}