Pith Number

pith:QYJEINLJ

pith:2009:QYJEINLJ5IX44E76I3AQ4UUCDN

not attested not anchored not stored refs pending

An extension of an inequality for ratios of gamma functions

Bai-Ni Guo, Feng Qi

arxiv:0902.2513 v3 · 2009-02-15 · 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{QYJEINLJ5IX44E76I3AQ4UUCDN}

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	2026-05-18T04:18:13.155780Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8612443569ea2fce13fe46c10e52821b6b7bc3ff50ac881300740664d1ba27aa

Aliases

arxiv: 0902.2513 · arxiv_version: 0902.2513v3 · doi: 10.48550/arxiv.0902.2513 · pith_short_12: QYJEINLJ5IX4 · pith_short_16: QYJEINLJ5IX44E76 · pith_short_8: QYJEINLJ

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/QYJEINLJ5IX44E76I3AQ4UUCDN \
  | 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: 8612443569ea2fce13fe46c10e52821b6b7bc3ff50ac881300740664d1ba27aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90c50a894def835eadc26574d333a10b4b3a332ccc0d728d0ecc88de6c769180",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2009-02-15T01:52:21Z",
    "title_canon_sha256": "4181f005d4d8445c4ab7848bc88955b87c134773ddf9fda28db63b6eecea86e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.2513",
    "kind": "arxiv",
    "version": 3
  }
}