Pith Number

pith:3CNPKT5B

pith:2011:3CNPKT5BVFCSVSYOS6L33HVM6R

not attested not anchored not stored refs pending

Light-tailed asymptotics of stationary tail probability vectors of Markov chains of M/G/1 type

Hiroyuki Masuyama, Kentaro Daikoku, Tatsuaki Kimura, Yutaka Takahashi

arxiv:1110.4457 v4 · 2011-10-20 · 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{3CNPKT5BVFCSVSYOS6L33HVM6R}

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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	2026-05-18T03:14:17.759238Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d89af54fa1a9452acb0e9797bd9eacf47efc8a2d58c9a1a9c1e3adb39a21f922

Aliases

arxiv: 1110.4457 · arxiv_version: 1110.4457v4 · doi: 10.48550/arxiv.1110.4457 · pith_short_12: 3CNPKT5BVFCS · pith_short_16: 3CNPKT5BVFCSVSYO · pith_short_8: 3CNPKT5B

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/3CNPKT5BVFCSVSYOS6L33HVM6R \
  | 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: d89af54fa1a9452acb0e9797bd9eacf47efc8a2d58c9a1a9c1e3adb39a21f922

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2676c133f9398823b201af2aad194a38bb65baff6c9070dd647a7761366e15e7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-10-20T06:37:27Z",
    "title_canon_sha256": "fa30a5f5fd2ee5497ec6cced20ae8f69f5c3cb17b97b5f579b11ab9df49d09d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.4457",
    "kind": "arxiv",
    "version": 4
  }
}