Pith Number

pith:7CNKYQP6

pith:2011:7CNKYQP6ZU5MVRLBKWH4DXXO4W

not attested not anchored not stored refs pending

Intricacies of Dependence between Components of Multivariate Markov Chains: Weak Markov Consistency and Markov Copulae

Jacek Jakubowski, Mariusz Niew\k{e}g{\l}owski, Tomasz R. Bielecki

arxiv:1105.2679 v5 · 2011-05-13 · 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{7CNKYQP6ZU5MVRLBKWH4DXXO4W}

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	2026-05-18T03:31:31.084257Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f89aac41fecd3acac561558fc1deeee582f3bbf8bef7bfb8b7543c529167813a

Aliases

arxiv: 1105.2679 · arxiv_version: 1105.2679v5 · doi: 10.48550/arxiv.1105.2679 · pith_short_12: 7CNKYQP6ZU5M · pith_short_16: 7CNKYQP6ZU5MVRLB · pith_short_8: 7CNKYQP6

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/7CNKYQP6ZU5MVRLBKWH4DXXO4W \
  | 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: f89aac41fecd3acac561558fc1deeee582f3bbf8bef7bfb8b7543c529167813a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4437a877ca2eef46a80a37618c7b274c93fa810d06d125bef446edcdbd40d925",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-05-13T10:02:41Z",
    "title_canon_sha256": "73f4d733b1e683e110fac05a2f1f350534a58fc9afde896d02c9fc0d51047863"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.2679",
    "kind": "arxiv",
    "version": 5
  }
}