Pith Number

pith:3NFHSXYI

pith:2014:3NFHSXYIGU3ZIN43VBJ5WD6X6Y

not attested not anchored not stored refs pending

Five remarks about random walks on groups

Michael Bj\"orklund

arxiv:1406.0763 v2 · 2014-06-03 · math.DS · 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{3NFHSXYIGU3ZIN43VBJ5WD6X6Y}

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	2026-05-18T02:48:16.978989Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db4a795f08353794379ba853db0fd7f62cf70b1da32f99aeb7608469469c8346

Aliases

arxiv: 1406.0763 · arxiv_version: 1406.0763v2 · doi: 10.48550/arxiv.1406.0763 · pith_short_12: 3NFHSXYIGU3Z · pith_short_16: 3NFHSXYIGU3ZIN43 · pith_short_8: 3NFHSXYI

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/3NFHSXYIGU3ZIN43VBJ5WD6X6Y \
  | 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: db4a795f08353794379ba853db0fd7f62cf70b1da32f99aeb7608469469c8346

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f1f680a18c844ad65cd8e1f61a77532f536a49bf2b227a60e5195d09992d613",
    "cross_cats_sorted": [
      "math.GR",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2014-06-03T15:53:48Z",
    "title_canon_sha256": "497cac5b2af354b51457223c5df4a42b13a30864dbd026a7be02155c7a09c57a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1406.0763",
    "kind": "arxiv",
    "version": 2
  }
}