Pith Number

pith:KZPPRGIY

pith:2015:KZPPRGIYPIHQFTUGZHM4IXDDAN

not attested not anchored not stored refs pending

Monotonicity of functions and sign changes of their Caputo derivatives

Kai Diethelm

arxiv:1510.03285 v2 · 2015-10-12 · 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{KZPPRGIYPIHQFTUGZHM4IXDDAN}

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	2026-05-18T01:15:32.360984Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

565ef899187a0f02ce86c9d9c45c63035cdef338edf563a144bc4537429212a1

Aliases

arxiv: 1510.03285 · arxiv_version: 1510.03285v2 · doi: 10.48550/arxiv.1510.03285 · pith_short_12: KZPPRGIYPIHQ · pith_short_16: KZPPRGIYPIHQFTUG · pith_short_8: KZPPRGIY

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/KZPPRGIYPIHQFTUGZHM4IXDDAN \
  | 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: 565ef899187a0f02ce86c9d9c45c63035cdef338edf563a144bc4537429212a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "011426a56363eff29e37cc3e6d1bd05ce1386abe930f230130eff1f9b4ea875e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-10-12T13:59:41Z",
    "title_canon_sha256": "061c1337e565ffc88151c2d97ab435e8ce2aa8bc901cdded15d5b4cf79eda67a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.03285",
    "kind": "arxiv",
    "version": 2
  }
}