Pith Number

pith:BMSNPSC6

pith:2013:BMSNPSC6YYJ37OSONSYVHJIRDS

not attested not anchored not stored refs pending

Asymptotic Analysis for Markovian Queues with Two Types of Nonpersistent Retrial Customers

Tuan Phung-Duc

arxiv:1312.0173 v2 · 2013-12-01 · 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{BMSNPSC6YYJ37OSONSYVHJIRDS}

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	2026-05-18T02:49:45.807942Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b24d7c85ec613bfba4e6cb153a5111ca5d40f4583318c5f7881d2cc0030fb80

Aliases

arxiv: 1312.0173 · arxiv_version: 1312.0173v2 · doi: 10.48550/arxiv.1312.0173 · pith_short_12: BMSNPSC6YYJ3 · pith_short_16: BMSNPSC6YYJ37OSO · pith_short_8: BMSNPSC6

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/BMSNPSC6YYJ37OSONSYVHJIRDS \
  | 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: 0b24d7c85ec613bfba4e6cb153a5111ca5d40f4583318c5f7881d2cc0030fb80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d7d3aa1256fb7a86fe7b8e4d68249aad5bb3bede84fb5a9334fbcb0dfe99e33",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-12-01T02:04:46Z",
    "title_canon_sha256": "bbcbab847eedc89903f91e371f64d4ca9b35191e1848ceccdd7e0305e1fa513f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.0173",
    "kind": "arxiv",
    "version": 2
  }
}