P. Bilokon

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math.GM2025

A Sieve on Rational Imbalances and the First Appearance of Denominators

Paul Alexander Bilokon

We construct a sieve that enumerates rational ``imbalances'' of the form $(p - q) / (p + q)$ for integers $p \geq 2$ and $1 \leq q < p$ , ordered lexicographically by $(p, q)$ . Each imbalance is…

math.GM2025

Simultaneous Novelty from First-Appearance Times in the Calkin-Wilf Enumeration

Paul Alexander Bilokon

We study the first-appearance map $I ¨ : N_{\geq 2} \to N_{0}$ that assigns to each denominator $d$ the earliest breadth-first index at which a reduced fraction of denomin…

math.GM2025

On the Density of Prime Imbalances in the Unit Interval

Paul Alexander Bilokon

We prove that the set of normalized differences between primes, defined as $S = {(p - q) / (p + q) : p > q are primes}$ , is dense in the open unit interval $(0, 1)$ . Our proof p…