Pith Number

pith:VLJ7TK36

pith:2026:VLJ7TK36PFANPIMJ2ZAAOEKW5L

not attested not anchored not stored refs pending

Fractional calculus via variable-transform-based spectral approximations

Kuan Xu, Xiaolin Liu

Variable transforms applied to Chebyshev polynomials yield stable spectral approximations for fractional integral operators.

arxiv:2604.25417 v3 · 2026-04-28 · math.NA · cs.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{VLJ7TK36PFANPIMJ2ZAAOEKW5L}

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.

Claims

C1strongest claim

These spectral approximations lead to stable and fast spectral methods for fractional calculus. The spectral approximation based on the double-exponential transform is demonstrated through extensive numerical examples that are intractable for existing spectral methods.

C2weakest assumption

The variable transforms are assumed to preserve spectral accuracy and numerical stability for the fractional integral operator without introducing hidden instabilities or requiring problem-specific tuning of the transform parameters.

C3one line summary

Variable-transform-based transplanted Chebyshev polynomials provide stable, optimal-complexity spectral approximations to fractional integrals, including Jacobi fractional polynomials and double-exponential variants applicable to broader problems.

Receipt and verification

First computed	2026-06-03T01:05:14.097612Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aad3f9ab7e7940d7a189d640071156eaf9903f10a2f929b3d78a9cd326944ac7

Aliases

arxiv: 2604.25417 · arxiv_version: 2604.25417v3 · doi: 10.48550/arxiv.2604.25417 · pith_short_12: VLJ7TK36PFAN · pith_short_16: VLJ7TK36PFANPIMJ · pith_short_8: VLJ7TK36

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/VLJ7TK36PFANPIMJ2ZAAOEKW5L \
  | 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: aad3f9ab7e7940d7a189d640071156eaf9903f10a2f929b3d78a9cd326944ac7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4223e273d65cf1b997437ee20e994f0be9f76fa6eed9240f2d877ab293ff69a",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-04-28T09:27:11Z",
    "title_canon_sha256": "1fc64f2a81808aa58084b49376bd41278a461acb1860d83e57102fc6aaa02d1f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.25417",
    "kind": "arxiv",
    "version": 3
  }
}