Impedance Mechanics: Gravity, Quantum Mechanics, and the Standard Model from the Mechanical Definition of Time

Impedance Mechanics derives gravity, quantum mechanics, and the Standard Model from a single mechanical definition of time: t = ∫s dx, where s is the metric slowness of the vacuum substrate. The vacuum is modelled as a six-degree-of-freedom micropolar (Cosserat) elastic continuum with three constitutive primitives — the substrate stiffness Yᵥ, the vacuum metric slowness s₀ = 1/c, and the vacuum impedance Z₀. The moto-temporal identity v·vₜ = 1, which follows directly from this definition, generates the Equivalence Principle, inertia, and gravitational time dilation as theorems. Newton's constant is derived as G = c⁴/ (8πYᵥ), Planck's constant as ℏ = YᵥL²ₜopo·s₀ where Lₜopo = √ (8π) ·lₚ follows from a temporal self-consistency condition, and all eight postulates of quantum mechanics follow from the substrate's wave mechanics without additional assumptions. The Standard Model gauge group U (1) ×SU (2) ×SU (3) is the automorphism group of the substrate's internal geometry. The charged lepton masses are derived via the Koide formula to better than 0. 01%, the Weinberg angle at the Z-pole to 0. 000%, the W and Z boson masses to 0. 14%, the QCD confinement scale to 0. 04%, and neutrino masses and oscillation splittings to better than 1%. Quark confinement is a theorem of the commutator structure. The number of fermion generations is the dimension of physical space. Cosmologically, the Universal Refractive Index γ = H₀, local/H₀, CMB = 1. 083179160 resolves the Hubble tension to 0. 001%. Dark matter is identified as longitudinal-only substrate polarization, yielding the exact Tully-Fisher relation vflat = (GMb·a₀) ^ (1/4) with no free parameters. The substrate exhibits shear-thinning viscoelastic behavior — Tchar (t) ∝ 1/ (γ−1) — giving the power-law relaxation γ (t) = 1 + K/t with K = 1. 2067 Gyr. This resolves the maturation paradox of high-redshift galaxies: JADES-GS-z14-0 (z = 14. 32) has a coordinate formation time of 77 Myr and a lookback time of 14. 43 Gyr, placing it 99. 5% of the way to the framework's hard observational horizon at Tchar = 14. 507 Gyr. Cloud 9 is identified as a pre-baryonic galactic halo in which baryonic matter has not yet reached the snap threshold. Six specific falsifiable predictions are made, including the annual drift of γ (5. 7×10⁻¹² yr⁻¹), the absolute neutrino mass scale (m_ν₁ = 0. 183 eV), and the hard observational horizon at Tchar = 14. 507 Gyr beyond which no lookback time can be observed. The framework contains no free parameters beyond its three constitutive primitives. Keywords: vacuum impedance, metric slowness, mechanical definition of time, temporal momentum, inertia, equivalence principle, Hubble tension, dark matter, gravity as timeshift, moto-temporal complement, unified field theory, micropolar substrate