What question did this study set out to answer?

The aim is to derive the Riemann spectrum using intrinsic phase space locking and explore implications for quantum computing.

February 10, 2026Open Access

Geometric Regularization of the Riemann Zeta Function via Intrinsic Phase Space Locking and Implications for Quantum Computing

Key Points

The aim is to derive the Riemann spectrum using intrinsic phase space locking and explore implications for quantum computing.
Derivation of the Riemann spectrum based on intrinsic phase space locking principles.
Application of Heisenberg Uncertainty constraints to the Berry-Keating Hamiltonian.
Numerical validation of the model to confirm accuracy.
The energy spectrum discretizes into the imaginary parts of the Riemann zeros.
Model validation shows a mean deviation error of less than 10^-5.
Implications for a novel scheme in Quantum Error Correction and vulnerabilities in RSA cryptography.

Abstract

The Riemann Hypothesis, linking the distribution of prime numbers to the non-trivialzeros of the Riemann Zeta function, remains one of the most significant open problems inmathematics. In this paper, we present a physical derivation of the Riemann spectrumbased on the principle of ”Intrinsic Phase Space Locking”. By imposing HeisenbergUncertainty constraints on the Berry-Keating Hamiltonian (H = xp), we demonstrate thatthe continuous phase space is topologically compactified into a toroidal manifold, forcingthe energy spectrum to discretize exactly into the imaginary parts of the Riemann zeros.Numerical validation confirms this model with a mean deviation error of < 10−5. Furthermore,we analyze the technological implications of this locking mechanism, proposing anovel topological protection scheme for Quantum Error Correction and assessing the potentialvulnerability of RSA cryptography under this new spectral understanding.

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