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 (UE = UB) and orthogonality (E ⊥ B) of light, leading to the definition of an intrinsic electromagnetic phase θEM = 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 θEM of light. Core results established in Part 3: - θEM = 0. 25 (π/4) — intrinsic phase of electromagnetic waves, defined from the structural analogy with UE = UB- 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 UE = UB supports θEM 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 θEM and γ₀, and convergence of Ωₘ, 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.