Pith Number

pith:PSIP42HN

pith:2011:PSIP42HNJIVKENGWUZ4GHWFA32

not attested not anchored not stored refs pending

Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative

Delfim F. M. Torres, Ricardo Almeida, Shakoor Pooseh

arxiv:1112.0693 v1 · 2011-12-03 · math.CA · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PSIP42HNJIVKENGWUZ4GHWFA32}

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	2026-05-18T04:02:26.898997Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c90fe68ed4a2aa234d6a67863d8a0de85ea79b16961b752f1d6b3bd51173c0e

Aliases

arxiv: 1112.0693 · arxiv_version: 1112.0693v1 · doi: 10.48550/arxiv.1112.0693 · pith_short_12: PSIP42HNJIVK · pith_short_16: PSIP42HNJIVKENGW · pith_short_8: PSIP42HN

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/PSIP42HNJIVKENGWUZ4GHWFA32 \
  | 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: 7c90fe68ed4a2aa234d6a67863d8a0de85ea79b16961b752f1d6b3bd51173c0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9171f97621a97422220366c40c57615fa71457a943ecfedbd7bbc91eac6f98ba",
    "cross_cats_sorted": [
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-12-03T21:46:00Z",
    "title_canon_sha256": "78c6c0c89f4fc049543fc3d23a2d597853d033b5c4e2879ace055b995c47e657"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0693",
    "kind": "arxiv",
    "version": 1
  }
}