Pith Number

pith:BGEQ4DZ3

pith:2026:BGEQ4DZ34YIYPJ4DLXT62Q6RHL

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An algorithmic approach to direct spline products: procedures and computational aspects

Alessandra Sestini, Francesco Patrizi

Direct B-spline products are computed robustly by recasting the formula via the Oslo algorithm and factoring terms to cut costs.

arxiv:2601.17432 v2 · 2026-01-24 · math.NA · cs.NA

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\pithnumber{BGEQ4DZ34YIYPJ4DLXT62Q6RHL}

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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

We then recast the direct formula into an algorithmic framework based on the Oslo Algorithm and subsequently enhance it, through a factorization of the terms to be computed, to dramatically improve computational efficiency.

C2weakest assumption

That the factorization step preserves numerical stability for all knot vectors and degrees without introducing new cancellation errors or requiring extra safeguards beyond those discussed.

C3one line summary

A factorization-enhanced Oslo-algorithm procedure computes B-spline products directly, avoiding ill-conditioned systems and cutting computational cost compared with collocation.

Receipt and verification

First computed	2026-05-18T02:45:05.914789Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09890e0f3be61187a7835de7ed43d13aeac6bbc2ba7b1d29a30270f80b2e26a3

Aliases

arxiv: 2601.17432 · arxiv_version: 2601.17432v2 · doi: 10.48550/arxiv.2601.17432 · pith_short_12: BGEQ4DZ34YIY · pith_short_16: BGEQ4DZ34YIYPJ4D · pith_short_8: BGEQ4DZ3

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BGEQ4DZ34YIYPJ4DLXT62Q6RHL \
  | 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: 09890e0f3be61187a7835de7ed43d13aeac6bbc2ba7b1d29a30270f80b2e26a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "286e70341d2b28bc1c01ddc9b4027573cbdae8f367dd464de214f8a0457f85b8",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-01-24T12:07:27Z",
    "title_canon_sha256": "bc444e026e1f7069deb67e8574c0c630ba9360cef8da7bd9dbfd6f8094077909"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.17432",
    "kind": "arxiv",
    "version": 2
  }
}