The Transverse Slicing Operator IV: Emergence of Minkowski Spacetime and Special Relativity (Part IV of the ODD Series)

We derive the 4D spacetime structure experienced by particles in the Operator-Derived Dimension (ODD) framework. Rather than postulating Special Relativity, we show that it is the emergent low-energy symmetry of a 5D Anti-de Sitter (AdS5) bulk broken by the Transverse Slicing Operator ˆQ.We formally calculate the induced metric on the domain wall via the First Fundamental Form. We demonstrate that the localization of the P¨oschl-Teller soliton at w = 0 spontaneously breaks the bulk SO(2, 4) symmetry down to the Poincar´e group ISO(1, 3). Consequently, the constancy of the speed of light c and Lorentz invariance are not axioms, but geometric constraints imposed by the dimensional reduction of the vacuum.