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This research aims to derive key aspects of non-commutative quantumspacetime and its connections to the Riemann zeta function using the MDC-X dynamic engine.

June 10, 2026Open Access

Non-Commutative Arithmetic Spectral Triples: First-Principle Derivation of von Neumann Factors, Tomita–Takesaki Modular Flows, and the Riemann Zeta Spectral Duality from the MDC-X Dynamic Engine

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DMDillip Kumar MahapatraKLE University

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Implication

Randomized trial establishes direct links between arithmetic structures and quantum mechanics, suggesting novel unifying principles.

Key Points

This research aims to derive key aspects of non-commutative quantumspacetime and its connections to the Riemann zeta function using the MDC-X dynamic engine.
Constructed the weak-operator closure of localized 2-adic Collatz algebra to classify as a Type III1/99 von Neumann factor.
Developed an arithmetic Dirac operator from the quadratic regulator, defining a separable Hilbert space.
Evaluated the Connes-Chern character index to derive a non-commutative Fredholm index.
The structure reveals a unique Type III1/99 von Neumann factor, excluding Types I and II.
The modular deformation of the arithmetic Dirac operator perfectly aligns with the first five non-trivial Riemann zeta zeros.
The non-commutative Fredholm index equals unity, indicating absolute topological stability of the quantum spacetime.

Cite This Study

Dillip Kumar Mahapatra (2026) studied this question.

synapsesocial.com/papers/6a2900566f82f25be989ce6e https://doi.org/10.5281/zenodo.20592500

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Non-Commutative Arithmetic Spectral Triples: First-Principle Derivation of von Neumann Factors, Tomita–Takesaki Modular Flows, and the Riemann Zeta Spectral Duality from the MDC-X Dynamic Engine

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Cite This Study

Non-Commutative Arithmetic Spectral Triples: First-Principle Derivation of von Neumann Factors, Tomita–Takesaki Modular Flows, and the Riemann Zeta Spectral Duality from the MDC-X Dynamic Engine

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