Stage I of a Relativistic Consistency Program - Resolving the S8 Tension with a Minimal Late–Time Modification of Gravity.

A persistent internal inconsistency known as the S8 tension challenges the concordance cosmological model, with Cosmic Microwave Background data favoring a more strongly clustered universe than indicated by weak–lensing surveys. Rather than proposing a specific modified–gravity theory, this work implements the first stage of a falsifiable, staged consistency program designed to isolate the physical origin of late–time cosmic acceleration. Stage I of the program consists of three necessary empirical viability tests: background expansion consistency (A), growth consistency (B), and weak–lensing consistency with controlled amplitude identifiability (C1). Within this framework, a minimal, scale–independent late–time modification of the Poisson sector is introduced as a diagnostic deformation. A numerical analysis based on Planck 2018 and DES Y3 data shows that General Relativity exhibits a tension of 1.88σ with respect to late–time clustering measurements. By weakening the effective gravitational coupling to µ = 0.9605, corresponding to a suppression of approximately 4%, the reconstructed value of S8 converges exactly to the center of the DES Y3 confidence region, yielding a residual tension of 0.00σ. Stability tests and redshift–evolution scans demonstrate that the solution is smooth, scale–independent, and preserves the standard hierarchy of structure formation. All Stage I consistency conditions are therefore satisfied, defining a narrow empirical viability window. This result establishes the controlled target region in which the decisive Stage II (C2), based on tomographic reconstruction of the Newton and Weyl sectors, becomes maximally sensitive (see Ref. 18) to genuine relativistic inconsistencies.