Pith Number

pith:5QYCV5DP

pith:2018:5QYCV5DPERLHGW665TZ2ORGH6J

not attested not anchored not stored refs pending

Cutoff for product replacement on finite groups

Alex Zhai, Ryokichi Tanaka, Yuval Peres

arxiv:1805.05025 v1 · 2018-05-14 · 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{5QYCV5DPERLHGW665TZ2ORGH6J}

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	2026-05-18T00:16:04.042146Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec302af46f2456735bdeecf3a744c7f276bdf3eef6910a291bf74f9bf71b0fea

Aliases

arxiv: 1805.05025 · arxiv_version: 1805.05025v1 · doi: 10.48550/arxiv.1805.05025 · pith_short_12: 5QYCV5DPERLH · pith_short_16: 5QYCV5DPERLHGW66 · pith_short_8: 5QYCV5DP

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/5QYCV5DPERLHGW665TZ2ORGH6J \
  | 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: ec302af46f2456735bdeecf3a744c7f276bdf3eef6910a291bf74f9bf71b0fea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea191c18b28bd87346765136810a9b4677d8bf18c5439aef92bfd438ec00b0d1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-05-14T06:51:21Z",
    "title_canon_sha256": "8967b02359223b6e0e60ff71012be15388f1505bd0e5dfb47c1fd43090ddf3ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.05025",
    "kind": "arxiv",
    "version": 1
  }
}