Pith Number

pith:MOFO4QPF

pith:2013:MOFO4QPFF5NUXOZORAEDROOYYA

not attested not anchored not stored refs pending

Log-concavity of a Mixture of Beta Distributions

Xiaosheng Mu

arxiv:1312.2166 v1 · 2013-12-08 · math.PR · 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{MOFO4QPFF5NUXOZORAEDROOYYA}

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	2026-05-18T03:05:17.077768Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

638aee41e52f5b4bbb2e880838b9d8c01d49d499dc12efc43404407b4ffab383

Aliases

arxiv: 1312.2166 · arxiv_version: 1312.2166v1 · doi: 10.48550/arxiv.1312.2166 · pith_short_12: MOFO4QPFF5NU · pith_short_16: MOFO4QPFF5NUXOZO · pith_short_8: MOFO4QPF

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/MOFO4QPFF5NUXOZORAEDROOYYA \
  | 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: 638aee41e52f5b4bbb2e880838b9d8c01d49d499dc12efc43404407b4ffab383

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "518d6dcadd3201bfac54009159c38b3d80a4e4be35f59a54185e307a0a9f94cf",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-12-08T02:43:28Z",
    "title_canon_sha256": "c16aa4f1a0788b6f3773ccaf10a9373d1f4542546954b6926cd67e3986c84d83"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.2166",
    "kind": "arxiv",
    "version": 1
  }
}