Pith Number

pith:ZW57Z5RA

pith:2011:ZW57Z5RAYLYIYNTZ2IZ3IYG5KZ

not attested not anchored not stored refs pending

Running Markov chain without Markov basis

Akimichi Takemura, Hisayuki Hara, Satoshi Aoki

arxiv:1109.0078 v1 · 2011-09-01 · math.ST · math.AC · 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{ZW57Z5RAYLYIYNTZ2IZ3IYG5KZ}

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	2026-05-18T04:14:17.512242Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdbbfcf620c2f08c3679d233b460dd56525d2303ba1b2d4477295526a1b6377d

Aliases

arxiv: 1109.0078 · arxiv_version: 1109.0078v1 · doi: 10.48550/arxiv.1109.0078 · pith_short_12: ZW57Z5RAYLYI · pith_short_16: ZW57Z5RAYLYIYNTZ · pith_short_8: ZW57Z5RA

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/ZW57Z5RAYLYIYNTZ2IZ3IYG5KZ \
  | 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: cdbbfcf620c2f08c3679d233b460dd56525d2303ba1b2d4477295526a1b6377d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e7368a8c082fedbcbfa026650e9d4ef9877edfa748c29d4f77834d657ffee01",
    "cross_cats_sorted": [
      "math.AC",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2011-09-01T03:20:47Z",
    "title_canon_sha256": "7993f0f18822e138ba26d9346c76cca1e2d05d506691506b517b18576c1de9d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.0078",
    "kind": "arxiv",
    "version": 1
  }
}