Pith Number

pith:6ZTTAWFP

pith:2013:6ZTTAWFPZSMHPDLA263J3F2RF7

not attested not anchored not stored refs pending

Convergence of a Second Order Markov Chain

Liqun Qi, Shenglong Hu

arxiv:1307.6919 v1 · 2013-07-26 · math.NA · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6ZTTAWFPZSMHPDLA263J3F2RF7}

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	2026-05-18T03:17:33.433758Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f6673058afcc98778d60d7b69d97512fc9abca4f933a67cf58e3166c9d1dd112

Aliases

arxiv: 1307.6919 · arxiv_version: 1307.6919v1 · doi: 10.48550/arxiv.1307.6919 · pith_short_12: 6ZTTAWFPZSMH · pith_short_16: 6ZTTAWFPZSMHPDLA · pith_short_8: 6ZTTAWFP

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/6ZTTAWFPZSMHPDLA263J3F2RF7 \
  | 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: f6673058afcc98778d60d7b69d97512fc9abca4f933a67cf58e3166c9d1dd112

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8755aa2a30224bb57ad7c68d106ce98473232d2f7b1843f45d292e3f09b7380",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2013-07-26T04:29:52Z",
    "title_canon_sha256": "3f2fc4a0fad4dbb84842bb8c39d2a356be211b013f4b11dff1375d3445cbe8b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.6919",
    "kind": "arxiv",
    "version": 1
  }
}