Pith Number

pith:AWZWOAQM

pith:2011:AWZWOAQM4UOT55IQO7VGMCS474

not attested not anchored not stored refs pending

One dimensional Markov random fields, Markov chains and Topological Markov fields

Brian Marcus, Guangyue Han, Nishant Chandgotia, Ronnie Pavlov, Tom Meyerovitch

arxiv:1112.4240 v1 · 2011-12-19 · math.DS · 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{AWZWOAQM4UOT55IQO7VGMCS474}

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	2026-05-18T01:25:47.973422Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05b367020ce51d3ef51077ea660a5cff094abdf670ac5d9f92ffd5127ace34a3

Aliases

arxiv: 1112.4240 · arxiv_version: 1112.4240v1 · doi: 10.48550/arxiv.1112.4240 · pith_short_12: AWZWOAQM4UOT · pith_short_16: AWZWOAQM4UOT55IQ · pith_short_8: AWZWOAQM

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/AWZWOAQM4UOT55IQO7VGMCS474 \
  | 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: 05b367020ce51d3ef51077ea660a5cff094abdf670ac5d9f92ffd5127ace34a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a259f458df482b5eb1f6376eaf95689494ec189d8f59745443b70103b9ccfe3b",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-12-19T05:07:31Z",
    "title_canon_sha256": "254e11034aed1bca9d4d461d180c9a674acc32e5298be6a3ff9c47aaa40867d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4240",
    "kind": "arxiv",
    "version": 1
  }
}