Total Coherent Theory (TCT): Vacency Coherence, Emergent Lorentz Symmetry, and Cosmological Predictions including Low-ℓ CMB Modulations

Total Coherent Theory v2 (TCT-v2) presents a theoretical framework in which the vacuum is modeled as a coherent physical state rather than as a passive background. The theory introduces a coherent doublet field, Ψ= (ψ, λ), = (, ), Ψ= (ψ, λ), endowed with an Algebra of Total Coherence (ACT), and explores how spacetime propagation, effective constants and cosmological evolution may emerge from this coherent-vacuum structure. This version strengthens the cosmological sector of TCT by deriving a dynamical scaling relation between coherent-vacuum perturbations and a preferred low-multipole angular scale in the cosmic microwave background. Perturbing the coherent vacuum as Ψ (x⃗, t) =Ψ0+δΨ (x⃗, t), (x, t) =₀+ (x, t), Ψ (x, t) =Ψ0+δΨ (x, t), and using a quartic coherent potential, the framework obtains an effective perturbation mass mΨ2=2λΨ02. m_² = 2₀². mΨ2=2λΨ02. In a FLRW background, the transition between gradient-dominated and mass-dominated coherent perturbations selects a characteristic coherent wavenumber, kΨ=ηΨaeffmΨ, k_ = _ a ₄₅₅ m_, kΨ=ηΨaeffmΨ, which projects onto the last-scattering sphere as ℓTCT≃kΨχ∗. ₓ₂ₓ k_ _*. ℓTCT≃kΨχ∗. For a coherent scale kΨ∼10−3 Mpc−1k_ 10^-3\, Mpc^-1kΨ∼10−3Mpc−1, the predicted angular scale is ℓTCT∼17, ₓ₂ₓ 17, ℓTCT∼17, with a finite modulation width naturally mapping this value into the approximate interval 14≤ℓ≤2014 2014≤ℓ≤20. The expected observational signature is not a sharp spectral line, but a smooth low-ℓℓ modulation, with a negative CMB–Large Scale Structure residual amplitude corresponding to a valley-like suppression of correlation efficiency. The paper also discusses the emergence of Lorentz symmetry from a homogeneous coherent vacuum, formal vacuum-dependent effective constants G (Ψ) G () G (Ψ), α (Ψ) () α (Ψ), Λeff (Ψ) ₄₅₅ () Λeff (Ψ), limiting cases recovering GR, ΛCDM, scalar–tensor gravity, quintessence-like behavior and varying-constant frameworks, as well as explicit falsifiability conditions for the predicted low-ℓℓ modulation. The work is theoretical. It does not claim to prove the observed CMB anomaly, nor does it present a complete first-principles numerical derivation of ℓTCT=17 ₓ₂ₓ=17ℓTCT=17. Instead, it formulates a testable dynamical scaling prediction linking coherent-vacuum relaxation to a preferred low-ℓℓ cosmological signature. The observational test is intended to be developed in a separate companion analysis based on CMB–LSS residual spectra, component-separated CMB maps, Gaussian mock realizations and multipole-space statistics.