Cosmo-Holonomy: Weighted Path Dependence of Cosmological Inference under Nonlinear Time

Cosmological parameters such as the Hubble constant are not measured directly but are inferred through statistical procedures that aggregate observational data across redshift. This paper develops a mathematical framework showing that cosmological inference can exhibit pathway dependence when nonlinear cosmic time mappings interact with weighted observational pipelines. The inferred expansion rate is formulated as a weighted functional acting on the cosmic expansion history, and when different observational pathways apply distinct weighting kernels, the resulting estimates can differ even when the underlying cosmological dynamics remain unchanged. The resulting residual is defined as cosmo-holonomy, representing a geometric form of inference path dependence analogous to holonomy in differential geometry. This perspective suggests that part of the discrepancy between different measurements of the Hubble constant—commonly known as the Hubble tension—may arise from pathway-dependent inference effects rather than from a fundamental inconsistency in cosmic dynamics.