Pith Number

pith:2APHYMNT

pith:2014:2APHYMNTBNEMLOFQNYYFBKU5Y3

not attested not anchored not stored refs pending

Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment

Bert Zwart, Eleni Vatamidou, Ivo J.B.F. Adan, Maria Vlasiou

arxiv:1405.0138 v1 · 2014-05-01 · 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{2APHYMNTBNEMLOFQNYYFBKU5Y3}

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	2026-05-18T02:52:48.911232Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d01e7c31b30b48c5b8b06e3050aa9dc6c2f0fda351428662f5554e707b8c8fef

Aliases

arxiv: 1405.0138 · arxiv_version: 1405.0138v1 · doi: 10.48550/arxiv.1405.0138 · pith_short_12: 2APHYMNTBNEM · pith_short_16: 2APHYMNTBNEMLOFQ · pith_short_8: 2APHYMNT

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/2APHYMNTBNEMLOFQNYYFBKU5Y3 \
  | 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: d01e7c31b30b48c5b8b06e3050aa9dc6c2f0fda351428662f5554e707b8c8fef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e02a4bbc827a3e375c10c7e304cf1a85968fcdac6756c8944b5e549afedee41",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-05-01T11:42:40Z",
    "title_canon_sha256": "71d535e995d6a8480b4af7f110b0210a7c6dfe57f7c23e5b528dd917f9e74862"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1405.0138",
    "kind": "arxiv",
    "version": 1
  }
}