Pith Number

pith:QGXQKXHX

pith:2015:QGXQKXHXXAIPECXWZA5OZ7HOGD

not attested not anchored not stored refs pending

Conditional Markov Chains Revisited Part I: Construction and properties

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

arxiv:1501.05531 v2 · 2015-01-22 · 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{QGXQKXHXXAIPECXWZA5OZ7HOGD}

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	2026-05-18T01:25:47.321363Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81af055cf7b810f20af6c83aecfcee30e10192d5f84635464c2904af6d0df7f7

Aliases

arxiv: 1501.05531 · arxiv_version: 1501.05531v2 · doi: 10.48550/arxiv.1501.05531 · pith_short_12: QGXQKXHXXAIP · pith_short_16: QGXQKXHXXAIPECXW · pith_short_8: QGXQKXHX

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/QGXQKXHXXAIPECXWZA5OZ7HOGD \
  | 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: 81af055cf7b810f20af6c83aecfcee30e10192d5f84635464c2904af6d0df7f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a5730a1ef5b9ad628e6d81271a1f2983689868062d7004f10ceeda2dd807c24",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-01-22T15:20:41Z",
    "title_canon_sha256": "3ca8491abc9503f52498d91fbfb4687eefc309e21ce6cc57dd8d9ff48a9e8d10"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.05531",
    "kind": "arxiv",
    "version": 2
  }
}