Jorge Vicente Romero

Riemann's Dynamical Mirror: Zeros, Chaos, and the Homoclinic Action in Ruelle Determinants

What do chaotic dynamical systems reveal about the deepest mysteries of number theory? This paper presents an analytical and comparative essay based on recent advances in the behavior of the Ruelle determinant for exponential maps over Cantor sets. Through this analysis, we estab...

Riemann's Dynamical Mirror: Zeros, Chaos, and the Homoclinic Action in Ruelle Determinants

What do chaotic dynamical systems reveal about the deepest mysteries of number theory? This paper presents an analytical and comparative essay based on recent advances in the behavior of the Ruelle determinant for exponential maps over Cantor sets. Through this analysis, we estab...

Exponential: Final

This is the final. The last upload to zenodo. I finish. Complete.

The Branch Tree of the Logarithm

This paper establishes a unified bridge between complex dynamical systems, ergodic optimization, and geometric group theory. By demonstrating that three classical logarithmic pathologies—the real-axis seam, non-fiber transitions, and the Poincaré network—are manifestations of a s...

The Lyapunov Ground State of the Complex Exponential Map

In the framework of ergodic optimization for complex dynamical systems, determining the extremal Lyapunov exponents of periodic orbits remains a significant challenge. This paper fully resolves the problem of how weakly repelling a periodic orbit of the complex exponential map $z...

The Lyapunov Ground State of the Complex Exponential Map

In the framework of ergodic optimization for complex dynamical systems, determining the extremal Lyapunov exponents of periodic orbits remains a significant challenge. This paper fully resolves the problem of how weakly repelling a periodic orbit of the complex exponential map $z...

Exact Finite-Radius Reading of Logarithmic Terms in Irregular Singular Germs: A Matrix Pencil Approach

Logarithmic terms in Hukuhara–Turrittin germs at irregular singular points are classically treated as asymptotic obstructions to contour integration. This work completely overturns this view by establishing an exact, finite-radius reading law. We show that the logarithmic axis fo...

The Zeta Axis II: A Geometric Framework for Complex Analysis via Formal Puiseux Series and Exact Certification

This paper presents a comprehensive mathematical framework that reimagines classical complex analysis through the integration of a novel number system and its precise geometric visualization. By replacing the classical zero with an invertible infinitesimal unit $z$, we establish...

The Zeta Axis II: A Geometric Framework for Complex Analysis via Formal Puiseux Series and Exact Certification

This paper presents a comprehensive mathematical framework that reimagines classical complex analysis through the integration of a novel number system and its precise geometric visualization. By replacing the classical zero with an invertible infinitesimal unit $z$, we establish...

The Exponential Pairing and its Logarithmic Tower: A Unified Theory of Nilpotent Jets, the Geometry of $\ln(0)$, and the Fine Structure of $\zeta$ Zeros

We show that two independently proposed frameworks—the extension of $\mathbb{C}$ by a nilpotent direction $b^2=0$ to capture the singularity of $\ln(0)$, and the asymptotic boundary study of the limit $\lim_{u\to 0^+}(\ln u + 1/u)^u$—are two canonical specializations of a single...

THE MODULAR SPECTRAL ARCHITECTURE OF APÉRY'S CONSTANT: AN EXPLICIT FORMULA, CONTINUED-FRACTION FLUCTUATIONS, AND THE SEMI-CLOSED BRIDGE FROM GENERALIZED BERNOULLI NUMBERS ->*corrected*

Corrected version

Restricted Greedy Prime Decomposition, the Meissel-Mertens Constant, and a Structural Proof of the Riemann Hypothesis -----CORRECTION---

Version corrected.

THE MODULAR SPECTRAL ARCHITECTURE OF APÉRY'S CONSTANT: AN EXPLICIT FORMULA, CONTINUED-FRACTION FLUCTUATIONS, AND THE SEMI-CLOSED BRIDGE FROM GENERALIZED BERNOULLI NUMBERS ->*corrected*

Corrected version

The Slope Ratio $r = 360 ζ(3)2/π6$: Continued Fraction, Completed Zeta Values, and the Khinchin Giant

Corrected Version

A Level-Four Sum Rule and the Resolution of the Small-Gap Deficit of the Riemann Zeros: A High-Precision Computational Report

This computational report presents three novel findings regarding the local spacing and invariant structure of the nontrivial zeros of the Riemann zeta function, derived from high-precision evaluations at heights $\gamma$ ranging from $1.2 \times 10^4$ to $10^8$. Working within t...

The Slope Ratio $r = 360 ζ(3)2/π6$: Continued Fraction, Completed Zeta Values, and the Khinchin Giant

Corrected Version

A Level-Four Sum Rule and the Resolution of the Small-Gap Deficit of the Riemann Zeros: A High-Precision Computational Report

This computational report presents three novel findings regarding the local spacing and invariant structure of the nontrivial zeros of the Riemann zeta function, derived from high-precision evaluations at heights $\gamma$ ranging from $1.2 \times 10^4$ to $10^8$. Working within t...

An Exactly Solvable Alternating Pole Tower: Closed-Form Resurgence, Lambert W Asymptotics, and Perturbative Zeta Degeneracies

We present the comprehensive asymptotic and resurgent analysis of an alternating pole tower function characterized by non-isolated essential singularities. Unlike generic asymptotic models where exponential data must be numerically fitted, this system is exactly solvable simultan...

Restricted Greedy Prime Decomposition, the Meissel-Mertens Constant, and a Structural Proof of the Riemann Hypothesis -----CORRECTION---

Version corrected.

A Conditional Framework for the Riemann Hypothesis Via the Restricted Greedy Prime Decomposition Algorithm: Established Equivalences, the Critical Gap, and a Program for Closure

We present a complete conditional framework connecting the restricted greedy prime decomposition algorithm to the Riemann Hypothesis (RH). We prove four rigorous equivalences between the algorithmic error structure and analytic number theory. Three of the four implications in the...