Pith Number

pith:X3Y7DFJN

pith:2018:X3Y7DFJNZKBOLIZ7AP42LNB7ZX

not attested not anchored not stored refs pending

Coagulation with product kernel and arbitrary initial conditions: Exact kinetics within the Marcus-Lushnikov framework

Agata Fronczak, Micha{\l} {\L}epek, Pawe{\l} Kukli\'nski, Piotr Fronczak

arxiv:1809.04172 v5 · 2018-09-11 · cond-mat.stat-mech · physics.chem-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X3Y7DFJNZKBOLIZ7AP42LNB7ZX}

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	2026-05-17T23:56:47.246104Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bef1f1952dca82e5a33f03f9a5b43fcdcbe7faf2faba67aa8ad1e600694e8cca

Aliases

arxiv: 1809.04172 · arxiv_version: 1809.04172v5 · doi: 10.48550/arxiv.1809.04172 · pith_short_12: X3Y7DFJNZKBO · pith_short_16: X3Y7DFJNZKBOLIZ7 · pith_short_8: X3Y7DFJN

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/X3Y7DFJNZKBOLIZ7AP42LNB7ZX \
  | 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: bef1f1952dca82e5a33f03f9a5b43fcdcbe7faf2faba67aa8ad1e600694e8cca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "797e8d598a9a317703c1ff42ab84b9acdfb4262da7b6aa58140895aec2921b39",
    "cross_cats_sorted": [
      "physics.chem-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2018-09-11T21:19:36Z",
    "title_canon_sha256": "fdcadd7ab2142fcb0e48a9dc46f42031c485fe55f704560dec655afcdbd29cab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.04172",
    "kind": "arxiv",
    "version": 5
  }
}