Pith Number

pith:WSOQB2ZY

pith:2016:WSOQB2ZYWDXDRGTZ6Y45KAO6YG

not attested not anchored not stored refs pending

Monotonicity Results for Delta and Nabla Caputo and Riemann Fractional Differences via dual identities

Baahaaeldin Abdalla, Thabet Abdeljawad

arxiv:1601.05510 v1 · 2016-01-21 · math.DS · 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{WSOQB2ZYWDXDRGTZ6Y45KAO6YG}

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	2026-05-18T01:22:13.649168Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b49d00eb38b0ee389a79f639d501dec19ad13ec1e38f940dbcd8722af590bc40

Aliases

arxiv: 1601.05510 · arxiv_version: 1601.05510v1 · doi: 10.48550/arxiv.1601.05510 · pith_short_12: WSOQB2ZYWDXD · pith_short_16: WSOQB2ZYWDXDRGTZ · pith_short_8: WSOQB2ZY

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/WSOQB2ZYWDXDRGTZ6Y45KAO6YG \
  | 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: b49d00eb38b0ee389a79f639d501dec19ad13ec1e38f940dbcd8722af590bc40

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72f97b3376346f7a8cc529cb51d0397b266c399d043cc702aeeb4ba69f6b07ba",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2016-01-21T04:51:22Z",
    "title_canon_sha256": "0c808bc849b6561ecc59bdf1c82a1998a6a5004bcb9dd76556afb1a8b48a1814"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.05510",
    "kind": "arxiv",
    "version": 1
  }
}