Pith Number

pith:432EEAJ3

pith:2012:432EEAJ3Y4T7MM37THPBFSBN65

not attested not anchored not stored refs pending

Markov degree of the three-state toric homogeneous Markov chain model

Abraham Mart\'in del Campo, Akimichi Takemura, David Haws, Ruriko Yoshida

arxiv:1204.3070 v3 · 2012-04-13 · math.ST · math.CO · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{432EEAJ3Y4T7MM37THPBFSBN65}

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	2026-05-18T03:13:00.485983Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6f442013bc727f6337f99de12c82df76ead2c2e52281c8ab8919a6561444f20

Aliases

arxiv: 1204.3070 · arxiv_version: 1204.3070v3 · doi: 10.48550/arxiv.1204.3070 · pith_short_12: 432EEAJ3Y4T7 · pith_short_16: 432EEAJ3Y4T7MM37 · pith_short_8: 432EEAJ3

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/432EEAJ3Y4T7MM37THPBFSBN65 \
  | 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: e6f442013bc727f6337f99de12c82df76ead2c2e52281c8ab8919a6561444f20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6f4d447c7d46c749da3658dc054f0f4d47c037121544cf18fabb00a345a8d04",
    "cross_cats_sorted": [
      "math.CO",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2012-04-13T18:33:17Z",
    "title_canon_sha256": "d3e185b3a68b283de71ca4cc06fd23c2280690b97f3c7d9b6b7639c719082ce5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.3070",
    "kind": "arxiv",
    "version": 3
  }
}