Pith Number

pith:C2PDZVJ4

pith:2019:C2PDZVJ4NZODFTUPVDJ7K6BLEI

not attested not anchored not stored refs pending

Tail Asymptotics for the $M_1,M_2/G_1,G_2/1$ Retrial Queue with Priority

Bin Liu, Yiqiang Q. Zhao

arxiv:1901.05342 v1 · 2019-01-16 · 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{C2PDZVJ4NZODFTUPVDJ7K6BLEI}

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	2026-05-17T23:56:11.066301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

169e3cd53c6e5c32ce8fa8d3f5782b222370d11eeaf14978788fe92372c446b9

Aliases

arxiv: 1901.05342 · arxiv_version: 1901.05342v1 · doi: 10.48550/arxiv.1901.05342 · pith_short_12: C2PDZVJ4NZOD · pith_short_16: C2PDZVJ4NZODFTUP · pith_short_8: C2PDZVJ4

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/C2PDZVJ4NZODFTUPVDJ7K6BLEI \
  | 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: 169e3cd53c6e5c32ce8fa8d3f5782b222370d11eeaf14978788fe92372c446b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2e2b2ba2668da9a0251ef7ef6ff2c8f8047ab50b1ea3e83e30c6dd9f6154e6f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-01-16T15:24:31Z",
    "title_canon_sha256": "8aa906da2255202b6cd106e62cf2caaa12492e1c8028e3c85018f775bad3518c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.05342",
    "kind": "arxiv",
    "version": 1
  }
}