koideᵢnformationₜheoretic_

We propose an information-theoretic reinterpretation of the Koide formula Q = Σmₖ/ (Σ√mₖ) ² = 2/3 within the SOFT (Structured Observation Field Theory) framework. Under the Landauer principle, particle mass is proportional to a bit-count Nₖ, so that √mₖ becomes an information wavefunction amplitude ψₖ ∝ √Nₖ. 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: Qₗepton = 1/3 SU (2) uniform + 1/3 G₂ asymmetry = 2/3. The difference Qₗepton − Qboson = 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