Fiber-Aware Observable Cosmology on a Nonlinear Time Manifold

This work presents a fiber-aware formulation of observable cosmology defined on a nonlinear time manifold, where cosmic time is treated as a nontrivial function of clock time rather than a linear parameter. The framework is centered on a master observable function O(X), through which all cosmological measurements—supernovae, baryon acoustic oscillations, and the cosmic microwave background—are unified as weighted, path-dependent projections of a single underlying geometric structure. By introducing a nonlinear temporal connection, the theory naturally generates cosmo-holonomy, in which observable differences arise from transport along distinct pathways rather than from inconsistencies in physical laws. Without assuming a ΛCDM background, the approach provides a data-driven reconstruction of the expansion sector, revealing a regime-separated, endpoint-controlled shifted power law in true cosmic time. This formulation offers a unified geometric interpretation of major observational tensions and establishes a foundation for analyzing current and future cosmological datasets within a single coherent structure.