Pith Number

pith:V3FJTUX5

pith:2013:V3FJTUX5UVUH4RGTGOOHGRWUPI

not attested not anchored not stored refs pending

Markov degree of the Birkhoff model

Akimichi Takemura, Mitsunori Ogawa, Takashi Yamaguchi

arxiv:1304.1237 v3 · 2013-04-04 · 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{V3FJTUX5UVUH4RGTGOOHGRWUPI}

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	2026-05-18T02:48:10.040382Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aeca99d2fda5687e44d3339c7346d47a0a15a40b5106065fa44d4bc4c95a845b

Aliases

arxiv: 1304.1237 · arxiv_version: 1304.1237v3 · doi: 10.48550/arxiv.1304.1237 · pith_short_12: V3FJTUX5UVUH · pith_short_16: V3FJTUX5UVUH4RGT · pith_short_8: V3FJTUX5

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/V3FJTUX5UVUH4RGTGOOHGRWUPI \
  | 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: aeca99d2fda5687e44d3339c7346d47a0a15a40b5106065fa44d4bc4c95a845b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86cf7dc340890b8f85716b39adddcc862f085ed7a0dc342bbda7509696a7ae55",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2013-04-04T03:28:29Z",
    "title_canon_sha256": "5acbdd237d714274388c91d56aa4eaf90ba146c8e73eccdd16884b02ece92685"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.1237",
    "kind": "arxiv",
    "version": 3
  }
}