2025/01/01 by Jeanette Leue, Leue, Jeanette
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Quantum Mechanics and Applications #advanced mathematical theories
paper · doi:10.17605/osf.io/zfq7d
openalex publication_date 2025/01/01 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/15
This monograph establishes a unified ontological and mathematical framework for understanding discrete state transformations across mathematics, physics, and complex systems. The work identifies a fundamental gap in binary logic regarding developmental dynamics and proposes the Primarcode domain P = \0, 1, +1\ as the minimal necessary extension to accommodate state change. The central claim is that every realized transition requires a minimal act of realization, formalized as a Surplus Operator (+1), which acts upon a structured space of potentials to compel a unique outcome. By developing this distinction axiomatically, the work demonstrates that the universal increment x = y + 1 is not a domain-specific assumption but a structural necessity of any discrete system capable of change. Key Applications & Results: Quantum Mechanics: Reinterprets Schrödinger dynamics as the evolution of potential structures and provides a formal resolution to the measurement problem via the Observer-Modulator Framework, aligning with experimental decoherence data. Prime Number Mechanics: Introduces an arithmetic resonance framework where prime gaps act as frequencies. It presents a deterministic prime generation algorithm and a geometric embedding (the Prime Helix) that reveals the underlying mod-6 structure of the prime sequence. Riemann Hypothesis: Proposes the Leue Map and the Residual Whiteness Condition, establishing a computationally testable equivalence between the Riemann Hypothesis and the spectral completeness of prime-gap residuals. Topology & Cosmology: Provides a constructive proof for the 3-sphere as the necessary resonance arena for physical and arithmetic processes, offering new insights into the nature of space and Dark Energy. This work renders long-standing conceptual tensions—particularly in quantum measurement and number theory—transparent as necessary consequences of ontological structure.