Pith Number

pith:UFK7HSM4

pith:2022:UFK7HSM4LMRPXIZU6ZCQHXUUNH

not attested not anchored not stored refs pending

On the cycle maximum of birth-death processes and networks of queues

Richard J. Boucherie

arxiv:2205.15929 v1 · 2022-05-31 · 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{UFK7HSM4LMRPXIZU6ZCQHXUUNH}

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	2026-07-05T04:28:03.865843Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a155f3c99c5b22fba334f64503de9469e76d95786c9d30da1b104418c0bfac39

Aliases

arxiv: 2205.15929 · arxiv_version: 2205.15929v1 · doi: 10.48550/arxiv.2205.15929 · pith_short_12: UFK7HSM4LMRP · pith_short_16: UFK7HSM4LMRPXIZU · pith_short_8: UFK7HSM4

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/UFK7HSM4LMRPXIZU6ZCQHXUUNH \
  | 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: a155f3c99c5b22fba334f64503de9469e76d95786c9d30da1b104418c0bfac39

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f59fac9ac5072d8e7044f6be297305e1ea122c61b2ab8243fc7280f3a6f83cde",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2022-05-31T16:20:33Z",
    "title_canon_sha256": "f2cdce2aef0eef2811d7352762fcc663fd17bd3abe9663314c6df32059e9bf45"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2205.15929",
    "kind": "arxiv",
    "version": 1
  }
}