Pith Number

pith:JZY6CT73

pith:2015:JZY6CT73OY4SZGF7PL7AI2KDSL

not attested not anchored not stored refs pending

Bounds for the logarithm of the Euler gamma function and its derivatives

Armin Straub, Harold G. Diamond

arxiv:1508.03267 v1 · 2015-08-13 · 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{JZY6CT73OY4SZGF7PL7AI2KDSL}

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	2026-05-18T01:35:21.273134Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e71e14ffb76392c98bf7afe04694392dd152bca35cd2eb308e6e581c022c04a

Aliases

arxiv: 1508.03267 · arxiv_version: 1508.03267v1 · doi: 10.48550/arxiv.1508.03267 · pith_short_12: JZY6CT73OY4S · pith_short_16: JZY6CT73OY4SZGF7 · pith_short_8: JZY6CT73

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/JZY6CT73OY4SZGF7PL7AI2KDSL \
  | 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: 4e71e14ffb76392c98bf7afe04694392dd152bca35cd2eb308e6e581c022c04a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6168228d4172bf0f83511c9383ffa5cf209053eea7955eda30416e4c31134c6f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-08-13T16:50:52Z",
    "title_canon_sha256": "5e6db8b92d65cda496484dbb1dcd9265842020aec0f927ae550dda9a0c7df603"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.03267",
    "kind": "arxiv",
    "version": 1
  }
}