Pith Number

pith:M4LULR7S

pith:2009:M4LULR7S4J5JOMB3YUCMUHSNET

not attested not anchored not stored refs pending

Necessary and sufficient conditions for a function involving divided differences of the di- and tri-gamma functions to be completely monotonic

Bai-Ni Guo, Feng Qi

arxiv:0903.3071 v1 · 2009-03-18 · 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{M4LULR7S4J5JOMB3YUCMUHSNET}

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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	2026-05-18T01:11:44.091336Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

671745c7f2e27a97303bc504ca1e4d24ef01b634ebb70ebbe6bf623b6ff2e4f4

Aliases

arxiv: 0903.3071 · arxiv_version: 0903.3071v1 · doi: 10.48550/arxiv.0903.3071 · pith_short_12: M4LULR7S4J5J · pith_short_16: M4LULR7S4J5JOMB3 · pith_short_8: M4LULR7S

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/M4LULR7S4J5JOMB3YUCMUHSNET \
  | 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: 671745c7f2e27a97303bc504ca1e4d24ef01b634ebb70ebbe6bf623b6ff2e4f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5610cec099771189dc11e8202694098fa6328b4de7ff76563ce6898393beb11c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2009-03-18T01:28:45Z",
    "title_canon_sha256": "f19b79b1a40615b3e2294ba13baf6df8698b6c246297920c3ffba4749f89cede"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.3071",
    "kind": "arxiv",
    "version": 1
  }
}