Fractal Dynamic Theory of Everything (TOEFD) v2: Vibration, Entropic Echo, Quantization, and the Standard Model

We present the complete v2 extension of the Fractal Dynamic Theory of Everything (TOEFD), a framework built on a single closed string of Planck-scale radius oscillating at f₀ = c/lP ≈ 1. 855×10⁴³ Hz. The theory derives the full structure of spacetime, particle physics, and cosmology from four equations with no free parameters beyond G, c, ℏ, kB, lP. New in v2: Quantization via a closed Lagrangian yields two fundamental quanta — the dressed graviton and the entropon, a Planck-mass scalar. The cross-commutator Φ̂, χ̂ ≠ 0 is a new fundamental prediction establishing that gravity and entropy are not independent quantum observables. The entropon is identified as an ultra-cold CDM dark matter candidate produced by a gravitational FIMP mechanism, with cross-section σ ~ lP⁴ ~ 10⁻¹⁴⁰ m² — consistent with all null detection results. The cosmological constant is suppressed dynamically as Λ (t) = ΛP·exp (−4S (t) /kB), resolving the 122-order fine-tuning problem without adjustment. Inflation is replaced by entropic expansion, reproducing ns ≈ 0. 965 and predicting r ≈ 0. 002 — testable by LiteBIRD (2032). The Higgs field is identified with the entropon condensate, and Yukawa couplings are derived as yf (n, k) = 4GkBℏ/ (c·v²·lP) ·Fn·10⁻⁵ᵏ from the Fibonacci fractal structure. Three fermion generations are predicted from first principles via log₁₀₅ (mP/vEW) = 3. 34. Two-loop RGE running from mP to LHC scale reproduces top (1. 5%), bottom (6%), charm (9%), tau (5%) and muon (7%) masses without free parameters.