Pith Number

pith:AD3KLLR2

pith:2013:AD3KLLR2QBWTGIOK3L2SV5FIPL

not attested not anchored not stored refs pending

Asymptotic expansions of integral means and applications to the ratio of gamma functions

Lenka Vuk\v{s}i\'c, Neven Elezovi\'c

arxiv:1312.1500 v1 · 2013-12-05 · 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{AD3KLLR2QBWTGIOK3L2SV5FIPL}

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	2026-05-18T03:05:27.128312Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00f6a5ae3a806d3321cadaf52af4a87ae29ceedebddaebc10570b07719b37f93

Aliases

arxiv: 1312.1500 · arxiv_version: 1312.1500v1 · doi: 10.48550/arxiv.1312.1500 · pith_short_12: AD3KLLR2QBWT · pith_short_16: AD3KLLR2QBWTGIOK · pith_short_8: AD3KLLR2

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/AD3KLLR2QBWTGIOK3L2SV5FIPL \
  | 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: 00f6a5ae3a806d3321cadaf52af4a87ae29ceedebddaebc10570b07719b37f93

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce097c67074294d04a6ee5014cfc8e855800aa987d4c45b232917445ac64c46f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-12-05T10:54:34Z",
    "title_canon_sha256": "5012aaac249d4602d40b22d1663d7b7b9f4b1e2376bed424a14bb325faa6d91f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.1500",
    "kind": "arxiv",
    "version": 1
  }
}