Pith Number

pith:ACZK2O3L

pith:2013:ACZK2O3L43GFG2LENP6XR3PVGJ

not attested not anchored not stored refs pending

Inequalities and monotonicity properties for gamma and q-gamma functions

Martin E. Muldoon, Mourad E. H. Ismail

arxiv:1301.1749 v1 · 2013-01-09 · 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{ACZK2O3L43GFG2LENP6XR3PVGJ}

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	2026-05-18T03:36:56.001494Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00b2ad3b6be6cc5369646bfd78edf532472bfd05b7a99490ab4897a402d69307

Aliases

arxiv: 1301.1749 · arxiv_version: 1301.1749v1 · doi: 10.48550/arxiv.1301.1749 · pith_short_12: ACZK2O3L43GF · pith_short_16: ACZK2O3L43GFG2LE · pith_short_8: ACZK2O3L

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/ACZK2O3L43GFG2LENP6XR3PVGJ \
  | 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: 00b2ad3b6be6cc5369646bfd78edf532472bfd05b7a99490ab4897a402d69307

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d77b4b2f306bac64c4443f8bed9ac72e6f7e359aa4c7c23d8e8e2889dc964ee8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-01-09T03:52:57Z",
    "title_canon_sha256": "555d2e8b540fcd730490a9c37f3a71d9ca5d8fd9539e945ead1e483e33c32016"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.1749",
    "kind": "arxiv",
    "version": 1
  }
}