This submission presents a formal first-principles derivation demonstrating that the observational discrepancy known as the "Hubble Tension" is not indicative of new particle physics, but rather a scaling artifact arising from the application of a linear model (ΛCDM) to a non-linear causal topology. Using the Unified Applicable Time (UAT) and Unified Causal Principle (UCP) frameworks, we derive the effective matter density (Ω_m) and the dark energy density (Ω_Λ) from first principles, without recourse to free fitting parameters or ΛCDM-derived inputs. Methodology: The derivation uses three UAT/UCP constants (the Ivancho limit κ_crit = 4.978, the golden ratio φ ≈ 1.618, and the thermal calibration margin φ*/η = 0.07), three observational inputs independent of ΛCDM (T_CMB = 2.7255 K from COBE/FIRAS, η_B = 6.1×10⁻¹⁰ from Big Bang Nucleosynthesis, and H₀ = 73.04 km/s/Mpc from SH0ES), and standard physics (the Stefan-Boltzmann law, the blackbody photon distribution, and BBN abundances). Key equation: The effective matter density is derived as Ω_m(eff) = Ω_b × κ_crit × φ × (1 - φ*/η). Each factor has a precise physical interpretation: Ω_b is the bare baryon density from BBN, κ_crit is the maximum causal amplification (Ivancho limit), φ is the geometric phase resonance (golden ratio), and (1 - 0.07) is the efficiency after thermal dissipation. The dark energy density follows from geometric closure under the UAT prediction of exact spatial flatness: Ω_Λ = 1 - (Ω_m + Ω_r). Results: The derived values (Ω_m = 0.3133, Ω_Λ = 0.6867) match the Planck 2018 consensus values (Ω_m = 0.315 ± 0.007, Ω_Λ = 0.685 ± 0.007) with differences of 0.55% and 0.24% respectively. The apparent discrepancy in Ω_b (15%) is shown to be a direct consequence of the H₀ scaling effect: recalibrating the Planck baryon density from H₀ = 67.36 to H₀ = 73.04 km/s/Mpc yields Ω_b ≈ 0.0419, in agreement with the first-principles BBN calculation (0.04182). Implications: The results suggest that dark matter may not be an exotic particle but rather the causal friction imprint of baryonic matter, amplified by the geometric structure of the causal network. Dark energy emerges not as a fundamental constant but as the geometric remainder under exact spatial flatness. The Hubble Tension is resolved as a metric calibration artifact. The package includes the LaTeX manuscript and the Python script that reproduces all calculations.