Rodolfo Carneiro Moroz

The Bastard Child Analogy: Connecting Topology, Algebraic Cycles, and Cohomological Holes

The Hodge Conjecture stands as one of the most profound unsolved problems in mathematics, selected by the Clay Mathematics Institute as a Millennium Prize Problem. It populates the delicate interface between algebraic geometry and differential topology. This paper explores the hi...

The Galoisian Boundary: An Exploratory Critique of Higher-Dimensional Physics

This paper explores a novel epistemological perspective on the macroscopic dimensionality of physical spacetime, proposing that the Abel-Ruffini theorem may serve as a structural blueprint rather than a mere artifact of algebraic notation. We introduce the exploratory Tripartite...

A BF-Theoretic Spectral Origin for the Yang–Mills Mass Gap: Internal Poincare Coercivity from a Universal Curvature Framework

The Yang-Mills mass gap problem remains one of the most important unresolved questions in mathematical physics. Existing approaches include lattice gauge theory, Schwinger-Dyson equations, functional renormalization group methods, geometric gauge theory, instanton methods, topolo...

Mitigating Synchrotron Photon Noise via Evanescent Bandgap Barriers for Laboratory Graviton Counting: A Conceptual Framework

The direct isolation of individual gravitons remains the ultimate frontier in quantum gravity. Recentbreakthroughs regarding the gravito-phononic effect have proven that macroscopic bulk acousticresonators cooled to their ground states can resolve single-graviton absorption via q...

Mitigating Synchrotron Photon Noise via Evanescent Bandgap Barriers for Laboratory Graviton Counting: A Conceptual Framework

The direct isolation of individual gravitons remains the ultimate frontier in quantum gravity. Recentbreakthroughs regarding the gravito-phononic effect have proven that macroscopic bulk acousticresonators cooled to their ground states can resolve single-graviton absorption via q...

The Ontology of Cooperation: Unifying Godel's Proof and the Prisoner's Dilemma in the Infinite Horizon

This paper proposes a formal unification between the metaphysical logic of Kurt Godel’s Ontological Proof and the dynamic outcomes of Game Theory through the Iterated Prisoner’s Dilemma. By employing higher-order modal logic, we demonstrate that pure selfishness is mathematically...

TGS THEORY: A CANDIDATE UNIFIED FRAMEWORK FOR GODEL INCOMPLETENESS, TURING UNDECIDABILITY, AND SHANNON INFORMATION

This work proposes a candidate unification of three fundamental limitation principles:G¨odel incompleteness, Turing undecidability, and Shannon information constraints. The centralobject of the theory is the resolutive deficit, defined textually as the difference between the info...

TGS THEORY: A CANDIDATE UNIFIED FRAMEWORK FOR GODEL INCOMPLETENESS, TURING UNDECIDABILITY, AND SHANNON INFORMATION

This work proposes a candidate unification of three fundamental limitation principles:G¨odel incompleteness, Turing undecidability, and Shannon information constraints. The centralobject of the theory is the resolutive deficit, defined textually as the difference between the info...