The Oscillating Worldline: Symplectic Involution, Topological Mass Generation, and the Geometric Resolution of Baryon Asymmetry

By introducing the Extended Equivalence Principle, this paper proposes a topological framework that reinterprets the kinematic null boundary in Special Relativity ($v \to c$) and the gravitational event horizon in General Relativity ($r \to r_s$) as isomorphic manifestations of a universal Null Topological Seam ($ds^2_\Sigma \to 0$). We posit that elementary particles do not terminate at these boundaries, but rather undergo a discrete topological transformation of their proper causal flow. By elevating the geometry to the complexified cotangent bundle, we demonstrate that intersecting this null boundary triggers a symplectic involution ($\Omega \to -\Omega$) governed by the topological Maslov index. This rigorously reverses the canonical Hamiltonian vector flow, acting as an exact geometric CPT inversion into a "Black Mirror'' bipartite topology while preserving the background metric ($g_{\mu\nu}$). Applied to gravitational collapse, the algebraic inversion of the Raychaudhuri expansion scalar ($\theta \to -\theta$) gracefully bypasses the Penrose singularity theorems, generating exact relativistic repulsive gravity. Crucially, this framework natively derives the Standard Model mass hierarchy and fundamental gauge parameters. Path-integral evaluations of the boundary's chiral projection dictate a strict trans-phasic transition probability, while evaluating the Bohr-Sommerfeld winding numbers and $\mathbb{Z}_3$ phase-space holonomy yields the exact Koide formula vacuum angle ($\delta = 2/9$) from first principles, with residual deviations rigidly mapped to 1-loop Electroweak radiative corrections. The bare fine structure constant ($\alpha_0 = 1/137$) is geometrically derived from the symmetric tensor product of the bulk Clifford algebra and a singular boundary zero-mode, which inherently models the mass-suppressed, chiral-restricted neutrino. Applying Călugăreanu’s theorem ($Lk = Tw + Wr$) to the boundary's chiral projection strictly requires the antichronous return trajectories to generate Writhe, self-braiding into stable $SU(3)_C$ Trefoil knots ($3_1$). The topological self-energy of this knot natively derives the hadronic mass gap ($\sim 1836 m_e$). Furthermore, a WKB expansion of the global wave functional across this bipartite manifold recovers the local Schrödinger equation while satisfying the timeless Wheeler-DeWitt constraint ($\hat{\mathcal{H}}_{tot}\Psi = 0$) as a strict topological symmetry, resolving the Problem of Time. Ultimately, we establish that the requisite cosmological antimatter is not missing, but is geometrically sequestered within this stable hadronic topology, rigorously resolving the Baryon Asymmetry.