Pith Number

pith:6FCXN7CR

pith:2013:6FCXN7CRZ2YA3D2BVI4X5M2R5S

not attested not anchored not stored refs pending

An expansion formula with higher-order derivatives for fractional operators of variable order

Delfim F. M. Torres, Ricardo Almeida

arxiv:1309.4899 v1 · 2013-09-19 · math.CA · math.NA · math.OC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6FCXN7CRZ2YA3D2BVI4X5M2R5S}

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	2026-05-18T03:08:46.682462Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f14576fc51ceb00d8f41aa397eb351ec9a59c8d1021baff633700c6f95034bef

Aliases

arxiv: 1309.4899 · arxiv_version: 1309.4899v1 · doi: 10.48550/arxiv.1309.4899 · pith_short_12: 6FCXN7CRZ2YA · pith_short_16: 6FCXN7CRZ2YA3D2B · pith_short_8: 6FCXN7CR

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/6FCXN7CRZ2YA3D2BVI4X5M2R5S \
  | 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: f14576fc51ceb00d8f41aa397eb351ec9a59c8d1021baff633700c6f95034bef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c1dee5808b863e82a89a8ef6741d651d63549def19df79849ca2343db31c585",
    "cross_cats_sorted": [
      "math.NA",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-09-19T09:07:02Z",
    "title_canon_sha256": "2f2c307a9a446cedef3805ac707fc6726c806a2c1165da10d0baa1f749e55bd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.4899",
    "kind": "arxiv",
    "version": 1
  }
}