Pith Number

pith:NWYSYAZV

pith:2009:NWYSYAZVM3AEZH55IQAMRV3ZQM

not attested not anchored not stored refs pending

Asymptotic Expansions for the Conditional Sojourn Time Distribution in the $M/M/1$-PS Queue

Charles Knessl, Qiang Zhen

arxiv:0907.2910 v1 · 2009-07-16 · math.CA · 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{NWYSYAZVM3AEZH55IQAMRV3ZQM}

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	2026-05-18T03:13:34.411353Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6db12c033566c04c9fbd4400c8d779833707d5cf61e6020918448066693bdebc

Aliases

arxiv: 0907.2910 · arxiv_version: 0907.2910v1 · doi: 10.48550/arxiv.0907.2910 · pith_short_12: NWYSYAZVM3AE · pith_short_16: NWYSYAZVM3AEZH55 · pith_short_8: NWYSYAZV

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/NWYSYAZVM3AEZH55IQAMRV3ZQM \
  | 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: 6db12c033566c04c9fbd4400c8d779833707d5cf61e6020918448066693bdebc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7163da2f1935f7798e21db8f263ad5afa56cf36c4a633a0828cbb36f90f8233a",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2009-07-16T19:41:21Z",
    "title_canon_sha256": "6bd87a33600675c9139811d03c2caed07aa11120ef142e16e3bca8253b6c86e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.2910",
    "kind": "arxiv",
    "version": 1
  }
}