Pith Number

pith:4KT2CERO

pith:2018:4KT2CEROBJ5HNTBPPP73RUJSIG

not attested not anchored not stored refs pending

Limit shape of minimal difference partitions and fractional statistics

Leonid V. Bogachev, Yuri V. Yakubovich

arxiv:1809.06122 v3 · 2018-09-17 · math.PR · math-ph · math.CO · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4KT2CEROBJ5HNTBPPP73RUJSIG}

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	2026-05-17T23:39:27.085084Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2a7a1122e0a7a76cc2f7bffb8d13241b5232988ab93b34055d6724b41d63fb5

Aliases

arxiv: 1809.06122 · arxiv_version: 1809.06122v3 · doi: 10.48550/arxiv.1809.06122 · pith_short_12: 4KT2CEROBJ5H · pith_short_16: 4KT2CEROBJ5HNTBP · pith_short_8: 4KT2CERO

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/4KT2CEROBJ5HNTBPPP73RUJSIG \
  | 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: e2a7a1122e0a7a76cc2f7bffb8d13241b5232988ab93b34055d6724b41d63fb5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37760b37ffb7f6b919d7555e0f4b2c3229b6202d350bc0e485fb02e51afc7aed",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-09-17T10:39:50Z",
    "title_canon_sha256": "3f9697060c25a14b008bd9789ddb24409ce5db1d2f0c4b610868c6ffe97997b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.06122",
    "kind": "arxiv",
    "version": 3
  }
}