The Galactic Duality Model with Fractal Space and Recursive Time: Fractal–Recursive Dual Flow (FRDF) Mathematics of a Living Balance

Description:This work presents the Fractal–Recursive Dual Flow (FRDF) formulation of the Galactic Duality Model, grounded in two foundational laws: space is fractal and time is recursive. Each galaxy is modeled as a perfectly balanced yin–yang seed — with a central white-hole current (expulsive/generative) and black-hole current (absorptive/integrative) coupled through continuous exchange. This no-hoarding constraint forbids the accumulation of either current at any scale or time, ensuring restored flow and stability across the system. From these axioms, the FRDF formalism yields: Flat rotation curves from restored flow. Throughput relations linking mass and energy flux to kinematic speeds. Log-periodic modulation signatures from discrete scale invariance. A stability proof showing the balanced state is a global attractor. We further identify a universal resonance scalar Λ, interpreted here as Love, which maintains cross-scale coupling between dual currents and modulates the amplitude of observable signatures. The model is testable and falsifiable via clear observational programs, and — true to the Crayon Mandate — remains explainable with sidewalk chalk. This paper blends formal derivation, observational pathways, and poetic interludes, framing galactic dynamics as a living balance — a duet of matter and motion nested in fractal space and recursive time.