bibkey: burkeharismadhavendra2025repeatedintegrals authors: Maxim R. Burke; Maleeha Haris; Madhavendra year: 2025 title: “Repeated integrals of increasing functions” doi: 10.48550/arXiv.2512.02151 url: https://arxiv.org/abs/2512.02151v1 claim: “Conjecture 1.2 asserts the original endpoint-jet property P_n for every nonnegative integer n; the source proves the cases n=0,1,2,3.” strata_touched: [] license: citation-only triage: anchor

Repeated integrals and endpoint jets

Maxim R. Burke, Maleeha Haris and Madhavendra, Repeated integrals of increasing functions, arXiv:2512.02151v1. Conjecture 1.2 states:

$(P_n)$ is true for all nonnegative integers $n$.

The preceding definition uses $C^n[0,1]$ functions whose $n$th derivative is nondecreasing and nonconstant. Endpoint derivatives are one-sided. The property requires openness of the entire attainable jet set and, for each attainable vector, one smooth witness satisfying all the specified finite and higher endpoint jets. Theorem 8.2 establishes the cases $n=0,1,2,3$.

The full statement and its canonical candidate are given in the canonical formal source. The follow-up arXiv:2512.23949v1 names this same property $Q_n$ and retains the all-order conjecture as Conjecture 2.5. Generic moment-cone mixture results in di Dio, arXiv:1804.07058v2, supply a related method; they do not state the literal endpoint-one and all-higher-zero assertion.

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DOI: https://doi.org/10.48550/arXiv.2512.02151

Source version: https://arxiv.org/abs/2512.02151v1

Conjecture 1.2 and the preceding definition of $(P_n)$, p. 2, specify the original all-order endpoint-jet assertion. Theorem 8.2 establishes the cases $n=0,1,2,3$; it does not assert the conjecture for every nonnegative integer.