Marco Mantovanelli

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math.NT2026

Prime-Exponent Transition Geometry and Divisor Barriers Between Consecutive Highly Composite Numbers

Marco Mantovanelli

Let $d (n)$ be the divisor function and let $H < H^{'}$ be consecutive highly composite numbers. We study directed unit moves between their prime-exponent vectors under the hard ceiling…

math.NT2026

The Subtractive Divisor Orbit: Unconditional Bounds, Parity Constraints, and a Conditional Framework

Marco Mantovanelli

Let $I ¨ (n)$ denote the number of positive divisors of $n$ . Starting from $n_{0} = x$ , consider the orbit $n_{j + 1} = n_{j} - I ¨ (n_{j})$ , and let $a (x)$ be its hitting time of zero. Although the…