Pith Number

pith:YOIF32KE

pith:2011:YOIF32KEKAQSV6K3BHIPDRHLTC

not attested not anchored not stored refs pending

Multimodality of the Markov binomial distribution

Derong Kong, Michel Dekking

arxiv:1102.3613 v1 · 2011-02-17 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YOIF32KEKAQSV6K3BHIPDRHLTC}

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	2026-05-17T23:41:13.853171Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3905de94450212af95b09d0f1c4eb98810a33a105bc49b5d6da2d8bff7e77c4

Aliases

arxiv: 1102.3613 · arxiv_version: 1102.3613v1 · doi: 10.48550/arxiv.1102.3613 · pith_short_12: YOIF32KEKAQS · pith_short_16: YOIF32KEKAQSV6K3 · pith_short_8: YOIF32KE

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/YOIF32KEKAQSV6K3BHIPDRHLTC \
  | 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: c3905de94450212af95b09d0f1c4eb98810a33a105bc49b5d6da2d8bff7e77c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5b640bf7c01ecb6d9ecfa4a8b33bf0bcc77e69afa8004441e5a45841df5c4c9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-02-17T16:01:41Z",
    "title_canon_sha256": "d2500da055509cb5946b5429818791f38227db57e24fffd6b22996b699353673"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.3613",
    "kind": "arxiv",
    "version": 1
  }
}