Pith Number

pith:OIIB752K

pith:2013:OIIB752KSLZFKGNQLGD5X4GIGG

not attested not anchored not stored refs pending

Complete monotonicity of a difference between the exponential and trigamma functions

Feng Qi, Xiao-Jing Zhang

arxiv:1303.1582 v1 · 2013-03-07 · 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{OIIB752KSLZFKGNQLGD5X4GIGG}

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	2026-05-18T02:50:34.172485Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

72101ff74a92f25519b05987dbf0c831984e2c407d765ed5d0be1e3f6bb7586b

Aliases

arxiv: 1303.1582 · arxiv_version: 1303.1582v1 · doi: 10.48550/arxiv.1303.1582 · pith_short_12: OIIB752KSLZF · pith_short_16: OIIB752KSLZFKGNQ · pith_short_8: OIIB752K

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/OIIB752KSLZFKGNQLGD5X4GIGG \
  | 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: 72101ff74a92f25519b05987dbf0c831984e2c407d765ed5d0be1e3f6bb7586b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "615e3bd49414f1afcae0af28a29ad1d45c2765125fed85dc7baab0b2b3161b95",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-03-07T00:49:41Z",
    "title_canon_sha256": "6d4192590a3ff95288b1404545170b1f0abb4b9d7bf83722ac517d9f1f03c931"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.1582",
    "kind": "arxiv",
    "version": 1
  }
}