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 wA = (1−σ) and wR = σ satisfy the exact complementarity relation wA + wR = 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 σc = ½ parameter-free from the normalization condition wA (σc) = wR (σc), 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 sin²θW = wR (σ*) = σ* = ⅓, yielding the mass ratio mW/mZ = √ (2/3) ≈ 0. 8165. A single perturbative correction factor ξ = 0. 6937 recovers the experimentally observed value sin²θW ≈ 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 = mH/√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^μₑff (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 (ALR = 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