The KOKU-Genki Fiber Bundle: Time as Ma-Energy Variation, Space as Its Fiber, and the Big Bang as Singularity-Free Phase Transition

A mathematically rigorous reformulation of four-dimensional spacetime (x,y,z,t) within the KOKU-Genki two-layer cosmological framework. Three central results: (1) Time t is defined as the cumulative variation of Ma energy density rho_Ma: dt = d(rho_Ma)/(d(rho_Ma)/dt). Where rho_Ma does not vary, time does not pass. (2) The KOKU Universe (time layer, base space R^1) and Genki Particle Universe (spatial layer, fiber R^3) are formalized as a fiber bundle E = M_koku x_{rho_Ma} M_genki. The fiber bundle structure is Lorentz-invariant: coordinate transformations act on the total space but preserve the fibration. (3) The Big Bang is reinterpreted as a phase transition at critical Ma density rho_critical (analogous to thermodynamic phase transitions), eliminating the GR singularity problem without modifying observational predictions. Additional results: arrow of time = direction of rho_Ma variation; pre-Big Bang state = pure KOKU-layer rho_Ma accumulation without material fiber; distant objects appear contracted and near objects expanded due to fiber density variation; stars = local phase transitions. GR emerges as the smooth-manifold limit of the fiber bundle. Includes formal adoption of 1990s pre-theoretical diagram as Figure 1.

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