Pith Number

pith:PGBCVZPJ

pith:2010:PGBCVZPJCTP2MVME6QLKRWASIC

not attested not anchored not stored refs pending

Smoluchowski's equation: rate of convergence of the Marcus-Lushnikov process

Eduardo Cepeda (LAMA), Nicolas Fournier (LAMA)

arxiv:1010.0598 v2 · 2010-10-04 · 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{PGBCVZPJCTP2MVME6QLKRWASIC}

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	2026-05-18T04:27:06.570412Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79822ae5e914dfa65584f416a8d81240ab74e64ebe3beae3fd8f86809b856a06

Aliases

arxiv: 1010.0598 · arxiv_version: 1010.0598v2 · doi: 10.48550/arxiv.1010.0598 · pith_short_12: PGBCVZPJCTP2 · pith_short_16: PGBCVZPJCTP2MVME · pith_short_8: PGBCVZPJ

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/PGBCVZPJCTP2MVME6QLKRWASIC \
  | 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: 79822ae5e914dfa65584f416a8d81240ab74e64ebe3beae3fd8f86809b856a06

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a359bf661fbf573917269e7a5adf49361c48cc143581fe2e371c072ed2927f4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-10-04T14:13:24Z",
    "title_canon_sha256": "4847ab471645bdf3baeda8d3d902cb6545cd8f170e9a2da688c22fa6feb18607"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.0598",
    "kind": "arxiv",
    "version": 2
  }
}