Pith Number

pith:MFZZULI6

pith:2012:MFZZULI6WRQSTHDWCEJKQYVIND

not attested not anchored not stored refs pending

One-Dimensional Birth-Death Process and Delbr\"{u}ck-Gillespie Theory of Mesoscopic Nonlinear Chemical Reactions

Hao Ge, Hong Qian, Yunxin Zhang

arxiv:1207.4214 v1 · 2012-07-17 · math.DS · cond-mat.stat-mech · 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{MFZZULI6WRQSTHDWCEJKQYVIND}

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	2026-05-18T03:43:39.961075Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61739a2d1eb461299c761112a862a868d7365a77387e66b2cae9d8777e5ae752

Aliases

arxiv: 1207.4214 · arxiv_version: 1207.4214v1 · doi: 10.48550/arxiv.1207.4214 · pith_short_12: MFZZULI6WRQS · pith_short_16: MFZZULI6WRQSTHDW · pith_short_8: MFZZULI6

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/MFZZULI6WRQSTHDWCEJKQYVIND \
  | 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: 61739a2d1eb461299c761112a862a868d7365a77387e66b2cae9d8777e5ae752

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fac7319a3874ee2ae10113128748ccde7c5e98fab479ed16adefb584aa639ed5",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-07-17T20:58:35Z",
    "title_canon_sha256": "7aab4d8f93de516d3c13a03ddfd57653e5a941e3c4b9015c070d953269b7f5a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.4214",
    "kind": "arxiv",
    "version": 1
  }
}