Pith Number

pith:G2S4AZNI

pith:2013:G2S4AZNIETWMO42NW45RAIILXS

not attested not anchored not stored refs pending

A logarithmically completely monotonic function involving the ratio of gamma functions

Feng Qi, Wen-Hui Li

arxiv:1303.1877 v2 · 2013-03-08 · math.CA · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{G2S4AZNIETWMO42NW45RAIILXS}

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	2026-05-18T01:37:21.868160Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

36a5c065a824ecc7734db73b10210bbcb97434783183b5024696f5de9fd56df2

Aliases

arxiv: 1303.1877 · arxiv_version: 1303.1877v2 · doi: 10.48550/arxiv.1303.1877 · pith_short_12: G2S4AZNIETWM · pith_short_16: G2S4AZNIETWMO42N · pith_short_8: G2S4AZNI

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/G2S4AZNIETWMO42NW45RAIILXS \
  | 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: 36a5c065a824ecc7734db73b10210bbcb97434783183b5024696f5de9fd56df2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "311fc317f4b780f90e4bd07fe227d55f9155aff47f16c8cf179f15ec992b9045",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-03-08T02:55:23Z",
    "title_canon_sha256": "9c220f8a302680299f74fc620af791d027d4982c7081035ad37ee6fa422aa08d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.1877",
    "kind": "arxiv",
    "version": 2
  }
}