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

We present Impedance Mechanics, a framework in which the mechanical definition of time t = ∫s dx — where s(x) is the metric slowness of the vacuum substrate — yields the moto-temporal identity v·vₜ = 1 as its immediate consequence. Applied to a six-degree-of-freedom micropolar elastic substrate characterized by three independent constitutive primitives (Yᵥ, s₀, Z₀), this foundation generates the known laws of physics as theorems with no free parameters. The fine structure constant α = Z₀/(2Rₖ) is derivable once ℏ is established; the topological loop Lₜₒₚₒ = √(8π)·lₚ follows from temporal self-consistency. The derivations include: Newton's constant G = c⁴/(8πYᵥ); the Equivalence Principle; all eight postulates of quantum mechanics (including the Born rule P = |ψ|², the exact coefficient ℏ/2 of the uncertainty principle, and the physical origin of the imaginary unit i); Maxwell's equations from the Z₀ coupling; the Standard Model gauge group U(1)×SU(2)×SU(3) as the automorphism group of the substrate's internal geometry; left-handed chirality of the weak force as a theorem of the positive-energy condition; and quark confinement as a theorem of the commutator structure of the confined degrees of freedom. The complete particle mass spectrum follows from the confinement theorem, which forces two complementary Koide formulae: free propagating excitations satisfy Q = 2/3 (leptons); color-neutral bound states satisfy Q = 1/3 (hadrons). All three charged lepton masses are predicted to better than 0.01%. The neutrino is identified as the torsional gear-play of the substrate (Volumetric Slip ζ = γ^(1/18)), giving the three neutrino masses and oscillation splittings. The QCD confinement scale ΛQCD = πmₑ/(αγ^(1/6)) = 217.08 MeV is within 0.04% of the world average. The Universal Refractive Index γ = H_₀,local/H_₀,CMB = 1.083179160 simultaneously resolves the Hubble tension (error 0.001%), the MOND acceleration threshold (error 0.10%), and identifies dark matter as longitudinal substrate polarization and dark energy as the substrate's restorative elastic pressure. The substrate exhibits shear-thinning viscoelastic behavior: γ(t) = 1 + K/t with K = 1.2067 Gyr. Six specific falsifiable predictions are made, including the secular drift of γ at 5.7×10⁻¹² yr⁻¹ and the linear growth of the Hubble tension with redshift.