Fractal Mechanics: A Unified Framework

We present Fractal Mechanics v2, a geometric framework that derives particle masses, force coupling constants, cosmological parameters, and the arrow of time from a single organizing principle: the universe as a 291-level cascade of temporal Fibonacci harmonics connecting the Planck scale to the cosmic horizon. The fundamental paradigm of FM v2: qubits do not rotate in hyperdimensional space — they oscillate between real and imaginary components at frequencies following the golden ratio cascade. This temporal harmonics framework unifies quantum entanglement, spin, isospin, and the irreversibility of time as projections of a single temporal structure. Key results: the 17 fundamental particle masses are derived with average precision 2% using zero free parameters for mass ratios; the fine structure constant is derived from cascade harmonics at 0.1% precision and newly interpreted as the fundamental spatio-temporal conversion ratio; the vacuum impedance is identified as the 14th Fibonacci number (0.07% precision); the Hubble tension is resolved at 4.36 sigma significance; the Big Bang is identified as the unique quantum white fountain in cosmic history; and dark matter is explained as extended fractal solitons resolving the three core CDM problems. FM v2 adds a formal Hopfield network derivation of gravity, a completion of Weinberg's 1976 asymptotic safety program, a testable Casimir correction, and a geometric explanation of why fundamental forces emerged sequentially from the Big Bang. Ten clear falsification criteria are provided with a 2026-2060 experimental roadmap. Keywords: fractal geometry, Fibonacci sequence, golden ratio, particle masses, force unification, dark matter, cosmology, topological quantum computing, qHIGT