What does this research mean for the field?

The Riemann Hypothesis is proven true by demonstrating that all non-trivial zeros of the Riemann zeta function lie on the critical line due to structural coherence requirements in physical systems. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.CHALLENGES_CONSENSUS.

What question did this study set out to answer?

To establish a complete proof of the Riemann Hypothesis using the Coherence Systems Model (MCS).

February 17, 2026Open Access

The Coherence Imperative: A Complete Proof of the Riemann Hypothesis via Spectral-Algebraic Unification

Key Points

To establish a complete proof of the Riemann Hypothesis using the Coherence Systems Model (MCS).
Developed the Coherence Systems Model (MCS) as a theoretical framework.
Analyzed the interactions between non-isomorphic fields and their identical zeta functions.
Connected algebraic invariants to quantum observables through Artin L-functions and Grothendieck motives.
Proved that the positioning of non-trivial zeros of the Riemann zeta function is structurally necessary.
Resolved the Perlis dilemma regarding non-isomorphic fields sharing identical zeta functions.
Confirmed that all zeros are located on the critical line.

Abstract

Este trabajo presenta un marco teórico novedoso, el Modelo de Sistemas de Coherencia (MCS), para abordar la Hipótesis de Riemann. El MCS demuestra que la ubicación de los ceros no triviales de la función zeta de Riemann no es simplemente una propiedad aritmética, sino una necesidad estructural que surge de los requisitos de coherencia de los sistemas físicos. Se resuelve el dilema de Perlis, mostrando que los campos no isomorfos pueden compartir funciones zeta idénticas. La demostración se eleva al nivel de las funciones L de Artin y los motivos de Grothendieck, estableciendo una correspondencia entre invariantes algebraicos y observables cuánticos, forzando la ubicación de todos los ceros en la línea crítica. Este trabajo es parte de un programa de investigación integral. Para publicaciones relacionadas, consulte: https: //zenodo. org/search? q=metadata. creators. personₒrₒrg. name: %22Quilez%20Zamora, %20Jaime%22

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The Coherence Imperative: A Complete Proof of the Riemann Hypothesis via Spectral-Algebraic Unification

Key Points

Abstract

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