Theory of Scalar Inversion: A Holographic Unification of Micro and Macro Scales via Logarithmic Symmetry in a Static Universe

The Theory of Scalar Inversion (TIE) proposes that the universe exhibits a fundamental logarithmic reflection symmetry across physical scales, from the Planck length (~1. 616e-35 m) to the observable diameter (~8. 8e26 m), spanning approximately 61. 74 orders of magnitude. The human scale (~1. 7 m) occupies a central symmetry point (~57%), acting as the inversion axis between microscopic and macroscopic regimes. We formally derive that the TIE inversion operator I: s -> lp²/s is algebraically equivalent to cosmological T-duality in the Gasperini-Veneziano Pre-Big Bang string cosmology framework (1991), under the identification of string length with Planck length (ls = lp). The shifted dilaton phi~ = phi - 3*ln (a) is shown to be exactly invariant under this transformation (verified symbolically), and the Gasperini-Veneziano action is exactly invariant under the TIE operator. The TIE solution branch corresponds to the Pre-Big Bang solution a (t) proportional to (-t) ^-1/sqrt (3). A key result identifies the displacement of the TIE symmetry axis from the geometric center (57% vs 50%) as a direct measurement of the shifted dilaton vacuum expectation value: phi~₀ = ln (10) * RL * (gammaEM - 0. 5) ~ 10. 98 where gammaEM is the Euler-Mascheroni constant and RL ~ 61. 74. The compactification correction required (DeltaK ~ 11. 3) is consistent with known KKLT and Large Volume Scenario flux compactification models (Kachru et al. 2003; Balasubramanian et al. 2005). Falsifiable predictions for the CMB power spectrum are derived: natural suppression at low multipoles (l < 30), logarithmic symmetry around l ~ 70, and an effective fractal dimension ~1. 57 in temperature fluctuations. These predictions are testable with CMB-S4, LiteBIRD, and Euclid.