What question did this study set out to answer?

The research aims to establish a comprehensive proof of the Riemann zeta function's properties using fractal holography.

April 1, 2026Open Access

A Fractal-Holographic Representation of the Riemann Zeta Function via a Self-Similar Operator — Part II: Full Hard-Analysis Proofs, Fredholm Determinant Study, High-Resolution Spectral Diagonalization and Variational Principle

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The research aims to establish a comprehensive proof of the Riemann zeta function's properties using fractal holography.
Conducted hard-analysis proofs to establish mathematical foundations.
Performed a Fredholm determinant study to analyze eigenvalues.
Utilized high-resolution spectral diagonalization on a large matrix.
Applied the variational principle to find energy minimizers.
Proved that d_H(φ) = 1/2 is the unique energy minimizer of the fractal energy functional.
Achieved spectral diagonalization with an error margin below 10^{-14}.

Implication

Demonstrates unique energy minimizer findings in fractal analysis, indicating new insights into mathematical frameworks.

Abstract

Version 5.2 (Final Companion Paper to V4.4) — 31 March 2026 Full hard-analysis proofs, Fredholm determinant study, high-resolution spectral diagonalization (N=4096, error < 10⁻¹⁴) and variational principle proving that d_H(φ) = 1/2 is the unique energy minimizer of the natural fractal energy functional. Companion to Version 4.4: https://zenodo.org/records/19325293 (DOI 10.5281/zenodo.19325293) This record contains: - Full PDF and LaTeX source of V5.2 - Python script to regenerate all figures - All high-resolution figures (V4.4 + energy landscape) - V4.4 .tex for completeness

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Cite This Study

Docshakal (2026) studied this question.

synapsesocial.com/papers/69ccb6fd16edfba7beb88b8b https://doi.org/10.5281/zenodo.19328610

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Implication

Demonstrates unique energy minimizer findings in fractal analysis, indicating new insights into mathematical frameworks.

A Fractal-Holographic Representation of the Riemann Zeta Function via a Self-Similar Operator — Part II: Full Hard-Analysis Proofs, Fredholm Determinant Study, High-Resolution Spectral Diagonalization and Variational Principle

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Implication

Abstract

Discussion

Cite This Study

A Fractal-Holographic Representation of the Riemann Zeta Function via a Self-Similar Operator — Part II: Full Hard-Analysis Proofs, Fredholm Determinant Study, High-Resolution Spectral Diagonalization and Variational Principle

Key Points

Implication

Abstract

Discussion

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