Pith Number

pith:VAXJR2IH

pith:2013:VAXJR2IH4A7N2LZUONHMYU72HT

not attested not anchored not stored refs pending

Product-form solutions for a class of structured multi-dimensional Markov processes

Ivo J.B.F. Adan, Johan S.H. van Leeuwaarden, Jori Selen

arxiv:1310.8114 v3 · 2013-10-30 · math.PR · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VAXJR2IH4A7N2LZUONHMYU72HT}

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	2026-05-18T01:31:21.617072Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a82e98e907e03edd2f34734ecc53fa3cd9d9608c10391b3c6e35e90801ed7fb8

Aliases

arxiv: 1310.8114 · arxiv_version: 1310.8114v3 · doi: 10.48550/arxiv.1310.8114 · pith_short_12: VAXJR2IH4A7N · pith_short_16: VAXJR2IH4A7N2LZU · pith_short_8: VAXJR2IH

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/VAXJR2IH4A7N2LZUONHMYU72HT \
  | 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: a82e98e907e03edd2f34734ecc53fa3cd9d9608c10391b3c6e35e90801ed7fb8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac7e4288ec3077dcc8d7de22e464f3cb58ff8bbb41b66bc8c86a1e735f576df1",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-10-30T12:15:09Z",
    "title_canon_sha256": "78c377cdb8050182faa8b3e52c068e1f4219766959547cbaf165b51d0192819a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.8114",
    "kind": "arxiv",
    "version": 3
  }
}