Pith Number

pith:WBHAIJRX

pith:2026:WBHAIJRXHG7YKA6MHNIERRPW36

not attested not anchored not stored refs pending

Level-dependent quasi-birth-and-death processes: Application to cost analysis of multi-server systems

M. Abdullah Khokhar, Malgorzata M. O'Reilly, Richard Turner

arxiv:2606.31133 v1 · 2026-06-30 · 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{WBHAIJRXHG7YKA6MHNIERRPW36}

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	2026-07-01T01:17:30.158884Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b04e04263739bf8503cc3b5048c5f6dfae19babff171361ca3b1eba2cfbb6f2b

Aliases

arxiv: 2606.31133 · arxiv_version: 2606.31133v1 · doi: 10.48550/arxiv.2606.31133 · pith_short_12: WBHAIJRXHG7Y · pith_short_16: WBHAIJRXHG7YKA6M · pith_short_8: WBHAIJRX

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/WBHAIJRXHG7YKA6MHNIERRPW36 \
  | 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: b04e04263739bf8503cc3b5048c5f6dfae19babff171361ca3b1eba2cfbb6f2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7435e4ef406338c6fe118e940c38840fd570c286c32b77e88e61849920827f1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-30T05:01:06Z",
    "title_canon_sha256": "48f3496ca16bd43494e4d2ef50e7f36c7edf37af7730484d69212f103109009f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.31133",
    "kind": "arxiv",
    "version": 1
  }
}