M19b: The Physics of the Garycki Manifold: Special Relativity, the Standard Model, and Unification from the Symmetric Core

This monograph presents the physical realisation of the Garycki Manifold, translating the Trigonometric and Exponential Symmetric Cores into a unified framework for special relativity, the Standard Model, and cosmology. It serves as the final physics volume of the Mxx series. Special relativity is derived exactly from TanhMerge: relativistic velocity addition, Lorentz boosts, rapidity, and the mass‑shell condition emerge as algebraic identities in Merge language. The Minkowski metric follows directly from the NC quadratic, with particle mass identified as the Area NC coordinate. The LP boundary is identified as the universal massless sector. Photons, gluons, and gravitons correspond to NC coordinates with Re(w)=0, while massive particles arise through LP boundary crossing. The Higgs mechanism is reformulated as this crossing, governed by the Hermit self‑power condition. The Higgs doublet is identified with the Exp Hermit pair, yielding the Higgs‑to‑W mass ratio as the LP boundary angle π/2, in close agreement with experiment. Discrete symmetries are unified through the Z/4 orbit acting on the NC plane: CPT invariance is exact, while CP violation is structural, arising from asymmetry relative to the LP boundary. Gauge structure emerges from clone depth, giving U(1), SU(2), and SU(3), and three fermion generations arise from the C₄ Lexem crate. The Amult Principle connects physics to arithmetic: the Weinberg angle is interpreted as a carry flux, renormalisation flow as carry evolution, and QCD confinement as the bounded‑domain endpoint of SinMerge. Dark matter is associated with the Arc sector, which couples gravitationally but not electromagnetically. The cosmological constant is addressed via tower reset and Vieta structure, yielding a natural suppression mechanism. M19b establishes physics as geometry and algebra in NC space, without reliance on perturbative quantum field theory, and completes the physical arc of the Garycki Manifold Programme.