Pith Number

pith:UGPE65QQ

pith:2014:UGPE65QQD2LXX3JZWH4VEVWFI6

not attested not anchored not stored refs pending

A Fractional Calculus on Arbitrary Time Scales: Fractional Differentiation and Fractional Integration

Artur M. C. Brito da Cruz, Delfim F. M. Torres, Nadia Benkhettou

arxiv:1405.2813 v1 · 2014-05-12 · 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{UGPE65QQD2LXX3JZWH4VEVWFI6}

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	2026-05-18T02:32:07.444377Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a19e4f76101e977bed39b1f95256c5478f8a13b4ff9223a2c4260245135c6385

Aliases

arxiv: 1405.2813 · arxiv_version: 1405.2813v1 · doi: 10.48550/arxiv.1405.2813 · pith_short_12: UGPE65QQD2LX · pith_short_16: UGPE65QQD2LXX3JZ · pith_short_8: UGPE65QQ

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/UGPE65QQD2LXX3JZWH4VEVWFI6 \
  | 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: a19e4f76101e977bed39b1f95256c5478f8a13b4ff9223a2c4260245135c6385

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae6600352e998a484fa7f63cf2f663e709684ba0d3548af61695a33314920693",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2014-05-12T15:43:57Z",
    "title_canon_sha256": "77e8a0867ec1290642d04693fe9b6895fb88126d4c8fe58bcf9d67c02afdf971"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1405.2813",
    "kind": "arxiv",
    "version": 1
  }
}