Pith Number

pith:CDK3UZYZ

pith:2014:CDK3UZYZLP2IQTFVUWVKSCLWYA

not attested not anchored not stored refs pending

Random walks on weakly hyperbolic groups

Giulio Tiozzo, Joseph Maher

arxiv:1410.4173 v2 · 2014-10-15 · math.GT · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CDK3UZYZLP2IQTFVUWVKSCLWYA}

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	2026-05-18T02:30:15.228099Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10d5ba67195bf4884cb5a5aaa90976c0181d429f8d7613faf9216b49d07a92e5

Aliases

arxiv: 1410.4173 · arxiv_version: 1410.4173v2 · doi: 10.48550/arxiv.1410.4173 · pith_short_12: CDK3UZYZLP2I · pith_short_16: CDK3UZYZLP2IQTFV · pith_short_8: CDK3UZYZ

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/CDK3UZYZLP2IQTFVUWVKSCLWYA \
  | 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: 10d5ba67195bf4884cb5a5aaa90976c0181d429f8d7613faf9216b49d07a92e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7be0c60ddffa1832cf13976478a993da3f387ec26466882b3efea756f662c4d7",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2014-10-15T19:15:34Z",
    "title_canon_sha256": "f1aa65c40936b6dbc6bd1060f998b5455143e2646e5f6981d9d6c2f3547c97e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.4173",
    "kind": "arxiv",
    "version": 2
  }
}