What question did this study set out to answer?

To provide an analytical, non-perturbative resolution to both the Riemann Hypothesis and the Hodge Conjecture using mirrored coordinate systems and topological regularization.

August 19, 2026Open Access

The Solution of In-Finity: Tri-Value Calibration, Orthogonal Vectors, and Modular Inversion (Part I: Analytical Number Theory & Topology)

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Authors

ABAlexander Booska

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Implication

Theoretical analysis demonstrates coordinate constraints on the Riemann zeta function and complex manifolds, suggesting analytical resolutions to two fundamental Millennium Prize problems.

Key Points

To provide an analytical, non-perturbative resolution to both the Riemann Hypothesis and the Hodge Conjecture using mirrored coordinate systems and topological regularization.
Extended Ramanujan divergent series regularization into a dual-polarity coordinate track to establish a zero-net-energy topological interface.
Evaluated the Riemann zeta function reflection equation at the s=0 boundary using an Infinitesimal Multiplicity Operator to evaluate indeterminate products.
Analyzed complex projective manifolds by decomposing complex algebraic cycles into geometric rational Hodge classes using cross-locked 2D vector pairs.
Demonstrated strict uniform convergence of concurrent positive and negative tracking paths, eliminating step-discontinuities and constraining all non-trivial zeta zeros to the critical line with real part 1/2.
Confirmed that complex algebraic cycles on complex projective manifolds decompose linearly into rational Hodge classes through geometric counterpair locking.

Cite This Study

Alexander Booska (2026) studied this question.

synapsesocial.com/papers/6a8563c403308d306e2d7127 https://doi.org/10.5281/zenodo.21971599

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Implication

Theoretical analysis demonstrates coordinate constraints on the Riemann zeta function and complex manifolds, suggesting analytical resolutions to two fundamental Millennium Prize problems.

The Solution of In-Finity: Tri-Value Calibration, Orthogonal Vectors, and Modular Inversion (Part I: Analytical Number Theory & Topology)

Discussion

Member takes

Implication

Key Points

Cite This Study

The Solution of In-Finity: Tri-Value Calibration, Orthogonal Vectors, and Modular Inversion (Part I: Analytical Number Theory & Topology)

Discussion

Member takes

Implication

Key Points

Cite This Study

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