Pith Number

pith:ESUZPE3X

pith:2012:ESUZPE3XVNT6RKYOD32BEZJ3NX

not attested not anchored not stored refs pending

Tail asymptotics for cumulative processes sampled at heavy-tailed random times with applications to queueing models in Markovian environments

Hiroyuki Masuyama

arxiv:1203.6574 v9 · 2012-03-29 · math.PR · math.ST · stat.TH

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ESUZPE3XVNT6RKYOD32BEZJ3NX}

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	2026-05-18T03:03:55.266395Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

24a9979377ab67e8ab0e1ef412653b6df2c4e7a962d3296e81f68d514b223597

Aliases

arxiv: 1203.6574 · arxiv_version: 1203.6574v9 · doi: 10.48550/arxiv.1203.6574 · pith_short_12: ESUZPE3XVNT6 · pith_short_16: ESUZPE3XVNT6RKYO · pith_short_8: ESUZPE3X

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/ESUZPE3XVNT6RKYOD32BEZJ3NX \
  | 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: 24a9979377ab67e8ab0e1ef412653b6df2c4e7a962d3296e81f68d514b223597

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07e0691121325fd6b4348344ad317eb2948e202c8d3c6f128d7985f08001cf55",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-03-29T16:21:04Z",
    "title_canon_sha256": "99f3e86ddfb5f309070bfc08ade8f3683aee5370c5e1f1df60fa281a6b7b4662"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.6574",
    "kind": "arxiv",
    "version": 9
  }
}