Pith Number

pith:XCK7MCWT

pith:2015:XCK7MCWTLMOHWCMUTJFPH6YG7T

not attested not anchored not stored refs pending

Verifiable Conditions for the Irreducibility and Aperiodicity of Markov Chains by Analyzing Underlying Deterministic Models

Alexandre Chotard, Anne Auger

arxiv:1508.01644 v4 · 2015-08-07 · 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{XCK7MCWTLMOHWCMUTJFPH6YG7T}

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	2026-05-17T23:54:42.055457Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b895f60ad35b1c7b09949a4af3fb06fcd840d24cae26c5d1675f389549fcc8a2

Aliases

arxiv: 1508.01644 · arxiv_version: 1508.01644v4 · doi: 10.48550/arxiv.1508.01644 · pith_short_12: XCK7MCWTLMOH · pith_short_16: XCK7MCWTLMOHWCMU · pith_short_8: XCK7MCWT

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/XCK7MCWTLMOHWCMUTJFPH6YG7T \
  | 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: b895f60ad35b1c7b09949a4af3fb06fcd840d24cae26c5d1675f389549fcc8a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bcc9d99c43258aaeab5aaa03557a1cf4f2c2b391c3851656df26487e057d6f01",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-08-07T09:52:27Z",
    "title_canon_sha256": "90bf3a8d99dd677c8c3a3daa3b00760c98376b6c48d7abd4fc740d580564d566"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.01644",
    "kind": "arxiv",
    "version": 4
  }
}