Pith Number

pith:7BTHPKDJ

pith:2011:7BTHPKDJ5MDH44SDB4SL3DXCP3

not attested not anchored not stored refs pending

Degree Bounds for a Minimal Markov Basis for the Three-State Toric Homogeneous Markov Chain Model

Abraham Martin del Campo, David Haws, Ruriko Yoshida

arxiv:1108.0481 v2 · 2011-08-02 · math.CO · math.ST · 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{7BTHPKDJ5MDH44SDB4SL3DXCP3}

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	2026-05-18T04:16:22.217689Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f86677a869eb067e72430f24bd8ee27ec1332c07d02ea800934f4057c7f41909

Aliases

arxiv: 1108.0481 · arxiv_version: 1108.0481v2 · doi: 10.48550/arxiv.1108.0481 · pith_short_12: 7BTHPKDJ5MDH · pith_short_16: 7BTHPKDJ5MDH44SD · pith_short_8: 7BTHPKDJ

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/7BTHPKDJ5MDH44SDB4SL3DXCP3 \
  | 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: f86677a869eb067e72430f24bd8ee27ec1332c07d02ea800934f4057c7f41909

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0ac866d8ed003550c5b582e485acea20257c0d3f085caf3be682b68362c1ebe",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-08-02T04:38:47Z",
    "title_canon_sha256": "56c1a30b53cad1d3999e6a23ec02d3d7a8b076fa0d14e70a7fb11f5b081eef49"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.0481",
    "kind": "arxiv",
    "version": 2
  }
}