Pith Number

pith:CI7J6KNJ

pith:2018:CI7J6KNJ65AICTH4URWXL7OHZB

not attested not anchored not stored refs pending

Second Order Asymptotic Properties for the Tail Probability of the Number of Customers in the M/G/1 Retrial Queue

Bin Liu, Yiqiang Q. Zhao

arxiv:1801.09607 v2 · 2018-01-29 · 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{CI7J6KNJ65AICTH4URWXL7OHZB}

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	2026-05-17T23:48:40.742435Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

123e9f29a9f740814cfca46d75fdc7c84ac942d596f754ca77c05131cf106a42

Aliases

arxiv: 1801.09607 · arxiv_version: 1801.09607v2 · doi: 10.48550/arxiv.1801.09607 · pith_short_12: CI7J6KNJ65AI · pith_short_16: CI7J6KNJ65AICTH4 · pith_short_8: CI7J6KNJ

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/CI7J6KNJ65AICTH4URWXL7OHZB \
  | 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: 123e9f29a9f740814cfca46d75fdc7c84ac942d596f754ca77c05131cf106a42

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fcb4bbd4877457b796e4be7727f9eb4476fe8d670c67a3c2864fc3c00e3055ac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-01-29T16:35:50Z",
    "title_canon_sha256": "5cab12da9ad9eca977be542a663dfca489262f53053be4dd67884f8336554d64"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.09607",
    "kind": "arxiv",
    "version": 2
  }
}