koide_information_theoretic_

We propose an information-theoretic reinterpretation of the Koide formula Q = Σm_k/(Σ√m_k)² = 2/3 within the SOFT (Structured Observation Field Theory) framework. Under the Landauer principle, particle mass is proportional to a bit-count N_k, so that √m_k becomes an information wavefunction amplitude ψ_k ∝ √N_k. This is in direct analogy with the Born Rule of quantum mechanics (P = |ψ|²), and provides the first quantum-information-theoretic explanation of why the square root of mass appears in the Koide denominator. We further compute the information-distribution ratio Q for the electroweak gauge bosons and find Q(W⁺, W⁻, Z) ≈ 1/3, traceable to SU(2)_L symmetry. The deviation from exactly 1/3 is shown to be a precise algebraic signature of the Weinberg mixing angle and electroweak symmetry breaking. This leads to a new structural decomposition: Q_lepton = 1/3 [SU(2) uniform] + 1/3 [G₂ asymmetry] = 2/3. The difference Q_lepton − Q_boson = 1/3 equals the pure G₂ octonion contribution dim(m)/dim(3)² − 1/3 = 1/3 from the Schur lemma. The Koide formula is thus not a numerical coincidence among lepton masses, but an information-theoretic invariant measuring the difference in information-distribution modes between G₂ octonion structure and SU(2) gauge symmetry. This paper is part of the SOFT research series. Both English and Korean versions are included. Korean title: 코이드 공식의 정보학적 재해석과 G₂–SU(2) 정보 분배 이중 구조 발견