PAPER-FBT08A: A Geometric Bridge from Berry Locked Symplectic Structure to Lorentzian Kinematics

This paper isolates the geometric bridge from the six-dimensional FractureBerryTension (FBT) carrier to four-dimensional Lorentzian kinematics. In the updated foundational formulation, the upstream carrier is the coherent-state symplectic readout B6 ≃ (CP1)3, ΩB = λ1Ω(1)FS + λ2Ω(2)FS + λ3Ω(3)FS , as established in FBT0A. On its regular torus locus this carrier admits a Hamiltonian T3-phase frame. FBT0B then identifies the observable relative-phase carrier as T2rel = T3/ΔU(1) ≃ U(1)3/U(1)diag, and the associated four-dimensional observable carrier as a local diagonal MarsdenWeinstein reduction Mred4,c = μ−1Δ (c)/ΔU(1). The present paper begins from this coherent-state and relative-phase geometry. It does not attempt to derive full relativistic dynamics. Instead, it uses an admissible (4+2) readout, an effective dual-phase Berry curvature, a selected residual phase evaluation direction, and a phaselocked vacuum clock readout to define an observer-invariant null propagation structure on theeffective observable sector M4. A temporal clarification is built into the construction. The vacuum clock used here is not a primitive background time, not merely the microscopic phase parameter before locking, and not the entropy-ordered cosmological arrow. It is the globally comparable clock readout of the Berry-locked vacuum sector. In the terminology of the OMEGA classification of temporality, FBT08A uses the effective Lorentzian time layer: the clock obtained after local phase clocks become globally comparable under phase locking. A central clarification is that the S-gate is not identified with the full dual-phase torus. The full relative phase sector remains two-dimensional. The S-mode is used here only as a distinguished one-dimensional readout line inside T2rel, allowing the effective Berry curvature to be evaluated into a scalar propagation functional. The main result is structural: under natural smoothness, nondegeneracy, locality, homogeneity, and isotropy assumptions in the Berry-locked vacuum regime, the resulting null propagation cone determines a Lorentzian conformal structure on M4, unique up to positive local rescaling. In the flat vacuum sector this conformal class admits a distinguished representative locallyisometric to Minkowski spacetime. Thus the paper supplies a kinematical bridge: (CP1)3 −→ T2rel −→ phase-locked vacuum clock readout −→ S-evaluated Berry readout −→ observer-invariant null con