Euler’s Number and the 24-42 Inversion Symmetry in Fractal Phase-Time: A Conceptual Mathematical Framework for Multi-Scale Temporal Branching
Euler’s Number and the 24-42 Inversion Symmetry in Fractal Phase-Time: A Conceptual Mathematical Framework for Multi-Scale Temporal Branching Author: Steven Willis Henderson ORCID: 0009-0004-9169-8148 Date: February 1, 2026 Abstract Euler’s constant (e) governs exponential growth, probability distributions, and the temporal evolution of quantum systems. This paper identifies a previously unexamined structural feature within the decimal expansion of e: a mirrored inversion relationship between its 24th and 42nd positions. We refer to this pattern as the Euler Inversion Symmetry (EIS). Although purely mathematical in nature, EIS exhibits properties consistent with: 1. fractal temporal structuring, 2. multi-branch evolution of dynamical systems, and 3. symmetry-breaking transitions observed in physical, biological, and computational processes. This paper does not propose new physical laws or technological mechanisms. Instead, it introduces a conceptual framework in which EIS s...
