Pith Number

pith:2BAG4I6B

pith:2015:2BAG4I6BS4T2CNLDXCWNV33IC5

not attested not anchored not stored refs pending

Normalized incomplete beta function: log-concavity in parameters and other properties

Dmitrii Karp

arxiv:1509.05120 v1 · 2015-09-17 · math.CA · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2BAG4I6BS4T2CNLDXCWNV33IC5}

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	2026-05-18T01:32:49.866885Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d0406e23c19727a13563b8acdaef6817773e41b2d5425e395a081dff382fda97

Aliases

arxiv: 1509.05120 · arxiv_version: 1509.05120v1 · doi: 10.48550/arxiv.1509.05120 · pith_short_12: 2BAG4I6BS4T2 · pith_short_16: 2BAG4I6BS4T2CNLD · pith_short_8: 2BAG4I6B

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/2BAG4I6BS4T2CNLDXCWNV33IC5 \
  | 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: d0406e23c19727a13563b8acdaef6817773e41b2d5425e395a081dff382fda97

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "386ab9e8fcf5e63cb17db6763886efb7857cd664fa7a9b6a3f3f6f5867ab651f",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-09-17T04:19:23Z",
    "title_canon_sha256": "8f2233a58de725f0082a408624c821f4274230c13f083a3c3f435da8efbc693e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05120",
    "kind": "arxiv",
    "version": 1
  }
}