Pith Number

pith:4IH3FK3G

pith:2015:4IH3FK3GUJBRDVKLAZZGTJLZSY

not attested not anchored not stored refs pending

Smoluchowski aggregation-fragmentation equations: Fast numerical algorithm for steady-state solution

Anna Bodrova, Nikolai Brilliantov, Vladimir Stadnichuk

arxiv:1503.02421 v2 · 2015-03-09 · physics.comp-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{4IH3FK3GUJBRDVKLAZZGTJLZSY}

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	2026-05-18T02:19:07.762225Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e20fb2ab66a24311d54b067269a579960f90ee32ca8bd65c02b30ab50e42c0e7

Aliases

arxiv: 1503.02421 · arxiv_version: 1503.02421v2 · doi: 10.48550/arxiv.1503.02421 · pith_short_12: 4IH3FK3GUJBR · pith_short_16: 4IH3FK3GUJBRDVKL · pith_short_8: 4IH3FK3G

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/4IH3FK3GUJBRDVKLAZZGTJLZSY \
  | 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: e20fb2ab66a24311d54b067269a579960f90ee32ca8bd65c02b30ab50e42c0e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd73ccbd58a2bcf40c7ad996579035e240a0552bd9896fd060c5802e7d523f45",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.comp-ph",
    "submitted_at": "2015-03-09T10:56:53Z",
    "title_canon_sha256": "c8dc741b6c5b2565fd1e205b6c8ee77424493b57369cbdcf28892ff02dd84ddc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.02421",
    "kind": "arxiv",
    "version": 2
  }
}