Pith Number

pith:QLXPP3KH

pith:2015:QLXPP3KHUS7CWEHCQPC6VZIEK6

not attested not anchored not stored refs pending

Some new inequalities for the gamma function

Xiaodong Cao

arxiv:1503.04972 v1 · 2015-03-17 · 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{QLXPP3KHUS7CWEHCQPC6VZIEK6}

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	2026-05-18T02:22:20.949035Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82eef7ed47a4be2b10e283c5eae504578a28acb21581c4885294e98d46dfd4b3

Aliases

arxiv: 1503.04972 · arxiv_version: 1503.04972v1 · doi: 10.48550/arxiv.1503.04972 · pith_short_12: QLXPP3KHUS7C · pith_short_16: QLXPP3KHUS7CWEHC · pith_short_8: QLXPP3KH

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/QLXPP3KHUS7CWEHCQPC6VZIEK6 \
  | 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: 82eef7ed47a4be2b10e283c5eae504578a28acb21581c4885294e98d46dfd4b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e10d20cc734874511a87dd1c262c201708b33575e94d217b494bd8456547885",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-03-17T10:02:30Z",
    "title_canon_sha256": "071d471fd96df5d18dc05262d79007f70c488257ad0192ffcc036502a5e7e374"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.04972",
    "kind": "arxiv",
    "version": 1
  }
}