The Methodological Antinomy of Fundamental Physics: The Paradox of Testing New Geometric and Non-Expanding Paradigms with Measurement Frameworks Derived from Older Assumptions

This paper identifies a fundamental and largely unexamined problem in contemporary fundamental physics: the systematic use of measurement and interpretation frameworks that were constructed under older theoretical assumptions to evaluate new and potentially paradigm-shifting ideas. In cosmology, quantities such as luminosity distances, the sound horizon, BAO scales, and CMB power spectra have been extensively processed through the FLRW metric and the assumption of physical spacetime expansion. In high-energy physics, precision observables and effective field theory analyses rest on frameworks optimized for quantum field theory in Minkowski spacetime. When new proposals — particularly those involving non-expanding geometries, higher-dimensional projection effects, or intrinsic geometric back-reaction — are confronted with these pre-processed quantities, the comparison itself becomes methodologically compromised. This situation creates a deep antinomy: new theoretical frameworks are expected to be tested against data, yet the data have already been interpreted through the very paradigms they challenge. The result is a structural disadvantage that is rarely acknowledged. This issue is particularly severe for frameworks such as the Unified Dimensional Cohesion Theory (UDCT), whose foundational mechanisms — higher-dimensional bidirectional projection, geometric back-reaction, and the reinterpretation of the Hubble constant as an intrinsic geometric relaxation rate — directly modify photon propagation and effective spacetime structure. These effects are precisely the kind that are assumed away or absorbed during standard data processing pipelines. Consequently, UDCT and similar geometric approaches are systematically disadvantaged when evaluated using existing cosmological and high-energy physics observables. This paper argues that a genuine evaluation of alternative frameworks requires not merely new theories, but a parallel reconstruction of the measurement and interpretation pipelines themselves. The problem is illustrated across both cosmological and collider physics contexts, and a broad program for methodological overhaul is proposed.