Complex Phase Cosmology: A Topological Attempt to Unify Cosmological Problems Using Euler's Identity and Juridical Structuring Methodology — Part 3: Phase Symmetry at θ = π/4 and the Geometric Analysis of Electromagnetic Waves (Light)

In Part 1, Euler's formula and the identity |e^(iπθ)|² = 1 were established as the language of phase transitions. In Part 2, this was extended into dynamics through the phase evolution function θ(z), phase tension γ(z), and the energy partition ratios cos²(πθ)/sin²(πθ). Parts 1 and 2, however, applied these tools only at the macroscopic cosmological scale. This study (Part 3) is the first chapter of application, applying the tools from Parts 1 and 2 to the structure of electromagnetic waves (light) — the most fundamental radiative energy in the universe — without introducing any new equations or physical laws. The 50:50 energy partition at θ = π/4 is shown to exhibit structural analogy withthe 1:1 energy symmetry (U_E = U_B) and orthogonality (E ⊥ B) of light, leading to the definition of an intrinsic electromagnetic phase θ_EM = 0.25. Building on Part 1 (DOI: 10.5281/zenodo.19158235) and Part 2 (DOI: 10.5281/zenodo.19215216), Part 3 moves from cosmological dynamics to the first physical application, identifying a macro-micro scale separation between the cosmic phase θ(z) and the intrinsic phase θ_EM of light. Core results established in Part 3:- θ_EM = 0.25 (π/4) — intrinsic phase of electromagnetic waves, defined from the structural analogy with U_E = U_B- E ↔ real axis, B ↔ imaginary axis — phase-scalar re-representation atop the Riemann-Silberstein complex vector (Silberstein, 1907)- c = Maximum Phase Rotation Rate — the speed of light interpreted as the upper limit of phase rotation permitted by the universe- Lorentz invariance of U_E = U_B supports θ_EM as a candidate topological invariant The macroscopic cosmic phase at the present universe is θ(0) = 0.309; the 50:50 symmetry point (θ = 0.25) is estimated to be reached in the future (z ≈ −0.83, assuming γ₀ = 0.15). Quantitative tests — including constraints between θ_EM and γ₀, and convergence of Ω_m,CPC,int(z) — are reserved for future research. This research applies Juridical Structuring Methodology to cosmology, crossing traditional academic boundaries to propose a strictly falsifiable scientific framework.