KIR-QER-Nezirov - Supplement III Dual Coding of Quantum Fluctuation

This Supplement III extends the QER–KIR bridge established in Supplement II by demonstrating that the two σ-dependent coefficients of the Fokker-Planck equation — the diffusion coefficient D(σ) = D₀·(1−σ) and the drift coefficient μ(σ) = μ₀·σ — constitute not merely two parameters of the same phenomenon, but encode physically orthogonal information on two complementary channels: an Amplitude Channel A(σ) = D₀·(1−σ), measuring ontological openness and the strength of quantum fluctuation, and a Rate Channel R(σ) = μ₀·σ, measuring causal closure and the temporal density of collapse acts. Section II establishes the formal channel structure. The normalized channel weights w_A = (1−σ) and w_R = σ satisfy the exact complementarity relation w_A + w_R = 1 for all σ ∈ [0,1], constituting a complete partition of σ-information. Their product defines the dimensionless channel overlap measure Κ(σ) = σ(1−σ) ∈ [0, ¼], which plays the role of a kinematic form factor in the electroweak effective potential of Supplement IV. Section III derives the critical point σ_c = ½ parameter-free from the normalization condition w_A(σ_c) = w_R(σ_c), identifying it as the exact channel transition. The inflection point of the signal-to-noise ratio SNR(σ) ∝ σ/√(1−σ), at which the rate of dominance change is maximal, is located at σ* ≈ ⅓. Section IV interprets the weak nuclear force as the physical manifestation of this channel transition. The σ-regime of the W and Z bosons (σ ≈ 0.1–0.5) coincides precisely with the amplitude-rate competition region, structurally accounting for their finite mass, their role as transition mediators, and the special status of the weak interaction among the four fundamental forces. Section VIII provides a three-stage quantitative derivation of the W/Z boson parameters. At tree level, the Weinberg angle is identified parameter-free as sin²θ_W = w_R(σ*) = σ* = ⅓, yielding the mass ratio m_W/m_Z = √(2/3) ≈ 0.8165. A single perturbative correction factor ξ = 0.6937 recovers the experimentally observed value sin²θ_W ≈ 0.2312 to within measurement accuracy. The Κ-potential U(σ) = Λ⁴·σ(1−σ) reproduces the structure of electroweak symmetry breaking, with the Higgs mass constraining the energy scale to Λ = m_H/√2 ≈ 88.6 GeV. The absolute mass scale remains explicitly open as a hierarchy problem. Section VIII.5 derives the V−A structure of charged weak currents from the discrete symmetry properties of both channels. The vector current V^μ (P-even) is assigned to the amplitude channel; the axial-vector current A^μ (P-odd) to the rate channel. The effective current J^μ_eff(σ) = (1−σ)V^μ − σA^μ is shown to be P-violating, T-conserving, and C-violating for all σ ∈ (0,1), with maximal parity violation (A_LR = 1) at the rate fixed point σ = 1. The negative sign before A^μ is derived from parity transformation properties and is not independently postulated. Section VIII.6 develops a systematic perturbation theory of nonlinear channel coefficients, establishing a parity selection rule that constrains the allowed correction terms: even-power corrections in (1−σ) for the diffusion coefficient, odd-power corrections in σ for the drift coefficient. Mixed-parity crosstalk terms vanish by spatial integration. All results follow from the three foundational KIR axioms and the fixed-point structure of Supplement II, with no free parameters beyond the single calibration ratio SNR = μ₀/√D₀ and the perturbative correction ξ. KIR-QER-Nezirov: Kinetically Induced Spacetime and Quantum Field Emergence of Reality — Complete Theoretical Framework with Supplements I–V. Zenodo. https://doi.org/10.5281/zenodo.18943890