Pith Number

pith:JJ3AF6G5

pith:2015:JJ3AF6G52GSWDIMJBJ4AMJMDC7

not attested not anchored not stored refs pending

Directional convexity and characterizations of Beta and Gamma functions

Janu sz Matkowski, Martin Himmel

arxiv:1505.01472 v1 · 2015-04-22 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JJ3AF6G52GSWDIMJBJ4AMJMDC7}

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	2026-05-18T02:16:49.190381Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a7602f8ddd1a561a1890a7806258317f94f03db78650974b71b40175d4f2497

Aliases

arxiv: 1505.01472 · arxiv_version: 1505.01472v1 · doi: 10.48550/arxiv.1505.01472 · pith_short_12: JJ3AF6G52GSW · pith_short_16: JJ3AF6G52GSWDIMJ · pith_short_8: JJ3AF6G5

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/JJ3AF6G52GSWDIMJBJ4AMJMDC7 \
  | 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: 4a7602f8ddd1a561a1890a7806258317f94f03db78650974b71b40175d4f2497

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a04bc65391200f806e537506f3eb2e79132687ffeb3c34df33e5517a6e141620",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-04-22T17:42:29Z",
    "title_canon_sha256": "6b37e39cc58b6932f9302fdf3678a6cc4fe095d0c251358422edcf0d6fe5b088"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.01472",
    "kind": "arxiv",
    "version": 1
  }
}