Pith Number

pith:QFZ4VMZP

pith:2026:QFZ4VMZP4VKSPSPOJPZLTSTPVA

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Optimal $C^{1,1}$ and Quasi-Optimal $C^2$ Monotone Interpolation with Curvature Control

Fushuai Jiang, Garving K. Luli

Monotone Hermite data admits an explicit quadratic-spline interpolant that achieves the smallest possible L^infty curvature among all C^{1,1} functions.

arxiv:2605.14302 v1 · 2026-05-14 · math.CA

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\pithnumber{QFZ4VMZP4VKSPSPOJPZLTSTPVA}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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 provide an explicit optimal construction in C^{1,1} given by quadratic splines by studying the optimal velocity profile. Moreover, given E = {x1,…,xN} and f:E→R (without derivatives), we also provide a formula to compute the corresponding trace seminorm inf{||F''||_L^∞ : F(x)=f(x) on E and F'≥0 everywhere}.

C2weakest assumption

That the global minimizer of ||F''||_L^∞ over monotone C^{1,1} Hermite interpolants is attained inside the subclass of quadratic splines whose pieces are determined by the optimal velocity profile analysis.

C3one line summary

Explicit optimal quadratic-spline construction for C^{1,1} monotone Hermite interpolation minimizing ||F''||_infty, plus a formula for the monotone trace seminorm and a controlled mollification to C^2.

References

25 extracted · 25 resolved · 0 Pith anchors

[1] Majid, and Jamaludin Md 2012

[2] Francesc Ar` andiga, Antonio Baeza, and Dionisio F. Y´ a˜ nez. A new class of non-linear monotone hermite interpolants.Advances in Computational Mathematics, 39:289–309, 2013 2013

[3] D. Azagra, E. Le Gruyer, and C. Mudarra. Explicit formulas forC 1,1 andC 1,ω conv extensions of 1-jets in Hilbert and superreflexive spaces.Journal of Functional Analysis, 274(10):3003–3032, 2018 2018

[4] Piecewise polynomial interpolation and approximation 1965

[5] Springer, New York, 1978 1978

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:10.083778Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8173cab32fe55527c9ee4bf2b9ca6fa8149bf767ab5566a8bb075d2cb2a38067

Aliases

arxiv: 2605.14302 · arxiv_version: 2605.14302v1 · doi: 10.48550/arxiv.2605.14302 · pith_short_12: QFZ4VMZP4VKS · pith_short_16: QFZ4VMZP4VKSPSPO · pith_short_8: QFZ4VMZP

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/QFZ4VMZP4VKSPSPOJPZLTSTPVA \
  | 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: 8173cab32fe55527c9ee4bf2b9ca6fa8149bf767ab5566a8bb075d2cb2a38067

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8a3f1831fd946d24251794d4b86501f3c49fda845e521b54bb0e89b078540b3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-05-14T03:08:39Z",
    "title_canon_sha256": "f8ed859ad530b47fa3bf83dc2c5c1c8ea40f7233452bcd458563150608e6bd14"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14302",
    "kind": "arxiv",
    "version": 1
  }
}