This paper introduces a novel framework for rigorously addressing the Riemann Hypothesis (RH) thr... more This paper introduces a novel framework for rigorously addressing the Riemann Hypothesis (RH) through the development of a "Dynamic Interval Collapse" methodology. By constructing analytically continuous functions that dynamically converge onto the critical line, we systematically isolate the non-trivial zeros of the Riemann zeta function. The approach eliminates off-critical-line contributions while preserving those on the critical line through an energy-based measure. The framework is supported by rigorous proofs, including the dynamic exclusion of off-critical-line points and the preservation of critical-line zeros. By integrating these components, the paper provides a comprehensive demonstration that all non-trivial zeros of the Riemann zeta function lie on the critical line, thereby validating the RH. This methodology not only offers new insights into the structure of the critical strip but also establishes a robust mathematical foundation for resolving one of the most profound problems in mathematics.
We introduce a novel framework for analyzing the distribution of zeros of the Riemann Zeta Functi... more We introduce a novel framework for analyzing the distribution of zeros of the Riemann Zeta Function, leveraging a methodology of dynamically collapsing intervals onto the critical line ℜ(s) = 1/2, with s = ℜ(s) + iℑ(s), and denoting ℑ(s) as γ for visual simplicity. The approach employs two functions, f (γ) = 1 2 − 1 γ and g(γ) = 1 2 + 1 γ , which define "filters" or "walls" that systematically narrow the critical strip 0 < ℜ(s) < 1 to the critical line as |γ| → ∞. Through rigorous analysis, we demonstrate that this dynamic collapse eliminates all points not on the critical line, leaving only non-trivial zeros. Key results include proofs of the exclusion of off-line points and the preservation of contributions solely from the critical line, supported by energy-based measures and contour integration arguments. This framework provides a new perspective on zero localization and serves as a systematic approach to proving the Riemann Hypothesis. The methodology highlights the interaction between analytic number theory, complex analysis, and dynamic systems, offering a promising path to further insights into the structure of ζ(s) and its critical zeros.
This paper introduces a novel framework for rigorously addressing the Riemann Hypothesis (RH) thr... more This paper introduces a novel framework for rigorously addressing the Riemann Hypothesis (RH) through the development of a "Dynamic Interval Collapse" methodology. By constructing analytically continuous functions that dynamically converge onto the critical line, we systematically isolate the non-trivial zeros of the Riemann zeta function. The approach eliminates off-critical-line contributions while preserving those on the critical line through an energy-based measure. The framework is supported by rigorous proofs, including the dynamic exclusion of off-critical-line points and the preservation of critical-line zeros. By integrating these components, the paper provides a comprehensive demonstration that all non-trivial zeros of the Riemann zeta function lie on the critical line, thereby validating the RH. This methodology not only offers new insights into the structure of the critical strip but also establishes a robust mathematical foundation for resolving one of the most profound problems in mathematics.
We introduce a novel framework for analyzing the distribution of zeros of the Riemann Zeta Functi... more We introduce a novel framework for analyzing the distribution of zeros of the Riemann Zeta Function, leveraging a methodology of dynamically collapsing intervals onto the critical line ℜ(s) = 1/2, with s = ℜ(s) + iℑ(s), and denoting ℑ(s) as γ for visual simplicity. The approach employs two functions, f (γ) = 1 2 − 1 γ and g(γ) = 1 2 + 1 γ , which define "filters" or "walls" that systematically narrow the critical strip 0 < ℜ(s) < 1 to the critical line as |γ| → ∞. Through rigorous analysis, we demonstrate that this dynamic collapse eliminates all points not on the critical line, leaving only non-trivial zeros. Key results include proofs of the exclusion of off-line points and the preservation of contributions solely from the critical line, supported by energy-based measures and contour integration arguments. This framework provides a new perspective on zero localization and serves as a systematic approach to proving the Riemann Hypothesis. The methodology highlights the interaction between analytic number theory, complex analysis, and dynamic systems, offering a promising path to further insights into the structure of ζ(s) and its critical zeros.
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Papers by Hansel Valdes