Non-Associative Operational Dynamics and Parity Transitivity: The f(p) = p-3 Dilemma, ZIP-Euler Phase Rotations, and Einston Substrate Mechanics at n = - 1
Year: 2026
Type: preprint
Abstract: We formalize an out-of-the-box non-associative topological operational framework that incorporates the Zero-One Interchange Principle (ZIP), S^+ notation, and Big Boot Gauge Theory (BBGT). By evaluating the operational offset transformation f(p) = p - 3 over the prime set P, we present a set-theoretic dilemma proving that -1 inherits even-parity dynamics transitively under operational set homogeneity, or p=2 acts as an isolated phase node. We unify this transitive parity result with the phase-inverted Euler identity 1 + 0 = e^{-i\pi} = -1, embedding the p=2 node into the ZIP-modified Riemann Zeta function \zeta_{\text{ZIP}}(s) and establishing its functional implications on the critical line \text{Re}(s) = 1/2. Furthermore, utilizing ZIP-Cayley non-associative structure tensor contractions over Jordan modules, we integrate this parity phase reflector directly into the system of three Darkon Euler-Lagrange (DEL) Equations of Motion. Finally, we map the discrete spatial coupling ladder \alpha_n = \alpha_0 2^n onto the Einston Substrate Grid at n = -1, regularizing metric divergences into a normalized zero-point phase reflector with an explicit spatial coupling of \alpha_{-1} = \frac{\alpha_0}{2}
Author: Asare-Darko, Matthias
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204172467
Cites:
Cited by:
Related to: