Pith Number

pith:VQR2OFNS

pith:2015:VQR2OFNSHMTN7O5FI7ZHJN6KD7

not attested not anchored not stored refs pending

On the joint behaviour of speed and entropy of random walks on groups

Gideon Amir

arxiv:1509.00256 v1 · 2015-09-01 · 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{VQR2OFNSHMTN7O5FI7ZHJN6KD7}

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	2026-05-18T01:34:14.692143Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac23a715b23b26dfbba547f274b7ca1fea31ca19d3bbd08fcdf3d537645072aa

Aliases

arxiv: 1509.00256 · arxiv_version: 1509.00256v1 · doi: 10.48550/arxiv.1509.00256 · pith_short_12: VQR2OFNSHMTN · pith_short_16: VQR2OFNSHMTN7O5F · pith_short_8: VQR2OFNS

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/VQR2OFNSHMTN7O5FI7ZHJN6KD7 \
  | 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: ac23a715b23b26dfbba547f274b7ca1fea31ca19d3bbd08fcdf3d537645072aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02e81d620292906ae32e8debbc192ee7428b261f886aa46c68a50af60e18fef4",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-09-01T12:26:28Z",
    "title_canon_sha256": "f43a215bbfe4b172a9fe44cbf414299d2308d24812167f85e366efcdae2b8788"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.00256",
    "kind": "arxiv",
    "version": 1
  }
}