4 citations · 6 across the 14 of their papers we have counts for
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Reciprocal LCM powers and Robin's criterion
Grant Molnar
For , we study the reciprocal LCM-power function \[ σ^{[κ]}_{-1}(n) := \sum_{d \mid n}μ(d)\,σ_{-1}(n / d)^κ. \] We determine its average and extremal orders. A natural Robin-…
Reliability Theory for AI Control
Grant Molnar
Reliability theory gives a mature language for layered systems, but its formal tools are not yet standard in frontier AI control. We apply them to Google DeepMind's defenses agains…
The Tropical Algebra of Binary-Tree Height
Grant Molnar
The binary-tree height recursion defines an algebra on , with join given by and product \[ a\star b=\max\{a,b\}+1. \] We show that w…
The Gregory function and its completed Gregory transform
Grant Molnar
We study the entire interpolation \[ \mathcal{G}(z)=\int_0^1 \binom{x}{z}\,dx \] of the Gregory coefficients. Its completion satisfies the positive Markov-transform identity \[ \fr…
Integral-Differential Calculus
Grant Molnar
We give an exposition of the Newton-Leibniz calculus. We begin by defining the integral as a limit of Riemann sums, verify the integrals of the standard catalog of functions by dir…
On the symmetry of evidential support
Grant Molnar
For events and , we have \[ \mathbb{P}(A\mid B) > \mathbb{P}(A\mid \neg B) \qquad\Longleftrightarrow\qquad \mathbb{P}(B\mid A) > \mathbb{P}(B\mid \neg A) \] whenever all fou…