Pith Number

pith:UGOP7YQZ

pith:2011:UGOP7YQZIIF7DYIKQENTWOEBHH

not attested not anchored not stored refs pending

Stochastic coalescence in logarithmic time

Eyal Lubetzky, Po-Shen Loh

arxiv:1101.3110 v2 · 2011-01-17 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UGOP7YQZIIF7DYIKQENTWOEBHH}

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	2026-05-18T02:22:52.152972Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a19cffe219420bf1e10a811b3b388139f513689f86a8d145bddddb401ea0eb6b

Aliases

arxiv: 1101.3110 · arxiv_version: 1101.3110v2 · doi: 10.48550/arxiv.1101.3110 · pith_short_12: UGOP7YQZIIF7 · pith_short_16: UGOP7YQZIIF7DYIK · pith_short_8: UGOP7YQZ

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/UGOP7YQZIIF7DYIKQENTWOEBHH \
  | 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: a19cffe219420bf1e10a811b3b388139f513689f86a8d145bddddb401ea0eb6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0ffd977a0ccc825b2fb466e19c651a07c203f4d020317189fdcb46e8f07f7a6",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-01-17T02:10:29Z",
    "title_canon_sha256": "6dc67fe620c510eb957d1094bcbbb70ae182f2a83f1ab938a6d74843d9fc36e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.3110",
    "kind": "arxiv",
    "version": 2
  }
}