Pith Number

pith:YQFXPN2U

pith:2010:YQFXPN2UJ4LBCUUEHYFGUL4HSS

not attested not anchored not stored refs pending

Two monotonic functions involving gamma function and volume of unit ball

Bai-Ni Guo, Feng Qi

arxiv:1001.1496 v1 · 2010-01-10 · 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{YQFXPN2UJ4LBCUUEHYFGUL4HSS}

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	2026-05-18T03:48:34.580615Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c40b77b7544f161152843e0a6a2f8794a354bd6f27012d0595ad412bd13105c4

Aliases

arxiv: 1001.1496 · arxiv_version: 1001.1496v1 · doi: 10.48550/arxiv.1001.1496 · pith_short_12: YQFXPN2UJ4LB · pith_short_16: YQFXPN2UJ4LBCUUE · pith_short_8: YQFXPN2U

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/YQFXPN2UJ4LBCUUEHYFGUL4HSS \
  | 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: c40b77b7544f161152843e0a6a2f8794a354bd6f27012d0595ad412bd13105c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab6877783fd530c09e6fb0175baa69a9cb4c4677545b1f6ba62159fc256d00d0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-01-10T10:36:20Z",
    "title_canon_sha256": "8ef0e909ed0a9ca05655bfdfd55d2b692a4f464385b68ebfb9f701b058a88183"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.1496",
    "kind": "arxiv",
    "version": 1
  }
}