Pith Number

pith:2EPMWEHT

pith:2018:2EPMWEHTWX66LGNDED4YSN7NV4

not attested not anchored not stored refs pending

Exact asymptotic formulae of the stationary distribution of a discrete-time 2d-QBD process: an example and additional proofs

Masahiro Kobayashi, Toshihisa Ozawa

arxiv:1805.04802 v4 · 2018-05-13 · 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{2EPMWEHTWX66LGNDED4YSN7NV4}

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	2026-05-18T00:10:16.746474Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d11ecb10f3b5fde599a320f98937edaf36c53c1da17cd1435862c3ff3161edc2

Aliases

arxiv: 1805.04802 · arxiv_version: 1805.04802v4 · doi: 10.48550/arxiv.1805.04802 · pith_short_12: 2EPMWEHTWX66 · pith_short_16: 2EPMWEHTWX66LGND · pith_short_8: 2EPMWEHT

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/2EPMWEHTWX66LGNDED4YSN7NV4 \
  | 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: d11ecb10f3b5fde599a320f98937edaf36c53c1da17cd1435862c3ff3161edc2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed9e3ba9258753ec7dee17c75e1eb9f13a48f831ca8fe3868a7ae41bf1c319b8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-05-13T01:03:44Z",
    "title_canon_sha256": "e22f23ce00711c6470b535ee78bffdba7f755548ce065185daf13e555940f4b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.04802",
    "kind": "arxiv",
    "version": 4
  }
}