Pith Number

pith:WF54NAO3

pith:2015:WF54NAO32EADXUXQOLOKREH3FR

not attested not anchored not stored refs pending

A Hilbert-Type Integral Inequality in the Whole Plane Related to the Hypergeometric Function and the Beta Function

Bicheng Yang, Michael Th. Rassias

arxiv:1512.04706 v1 · 2015-12-15 · 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{WF54NAO32EADXUXQOLOKREH3FR}

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	2026-05-18T01:24:19.620386Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b17bc681dbd1003bd2f072dca890fb2c4fe21f2b6ffe315bf8b2a7d60bd29142

Aliases

arxiv: 1512.04706 · arxiv_version: 1512.04706v1 · doi: 10.48550/arxiv.1512.04706 · pith_short_12: WF54NAO32EAD · pith_short_16: WF54NAO32EADXUXQ · pith_short_8: WF54NAO3

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/WF54NAO32EADXUXQOLOKREH3FR \
  | 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: b17bc681dbd1003bd2f072dca890fb2c4fe21f2b6ffe315bf8b2a7d60bd29142

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1e1fe180c06f912c06c08c38d2421a5323709ce3c6abcaf0e1803c90d9f900c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-12-15T10:18:23Z",
    "title_canon_sha256": "a6e2a3f83cb57c0fef76b679456fd2cbdb0fdf588a4c7c7c7ed02c17687900ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04706",
    "kind": "arxiv",
    "version": 1
  }
}