Pith Number

pith:MJV7QVDF

pith:2010:MJV7QVDFAYU564TUDNQC4OSJCL

not attested not anchored not stored refs pending

Generalized crested products of Markov chains

Alfredo Donno, Daniele D'Angeli

arxiv:1006.4872 v1 · 2010-06-24 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MJV7QVDFAYU564TUDNQC4OSJCL}

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	2026-05-18T01:20:54.226792Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

626bf854650629df72741b602e3a4912e5299d96f404f1a9db35b9aa759ed14d

Aliases

arxiv: 1006.4872 · arxiv_version: 1006.4872v1 · doi: 10.48550/arxiv.1006.4872 · pith_short_12: MJV7QVDFAYU5 · pith_short_16: MJV7QVDFAYU564TU · pith_short_8: MJV7QVDF

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/MJV7QVDFAYU564TUDNQC4OSJCL \
  | 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: 626bf854650629df72741b602e3a4912e5299d96f404f1a9db35b9aa759ed14d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92ede65a07b65e591ac58a7ca04a7d39ecd574b911a502364b1a5e9a0dacc058",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-06-24T20:23:13Z",
    "title_canon_sha256": "d5d437964a88ec3768aba46204c76f2b35c37c8589e9ec4fa0718f7144cfbaa7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.4872",
    "kind": "arxiv",
    "version": 1
  }
}