Triad Cosmology V.3: A Relational Framework for Late-Time Inhomogeneity and Observational Inference

This document presents Triad Cosmology V.3, a constraint-ready and falsifiable methodological framework designed to test whether large-scale cosmic inhomogeneities—particularly cosmic voids—can modulate the inference of late-time cosmic expansion without altering global cosmological dynamics. The framework preserves the standard ΛCDM background and general relativity, introducing no new fields or modifications to gravitational laws. Instead, it formalizes an environment-dependent modulation parameter that operates at the level of observational inference, decoupling global expansion physics from local structural context. Triad Cosmology V.3 is explicitly formulated for empirical constraint using upcoming large-scale structure data. It emphasizes ensemble-based structure definition, gravitational validation, probabilistic environmental association, and integrated null tests to ensure robustness and falsifiability. This document serves as a concise archival reference and methodological marker. Detailed derivations, numerical pipelines, and extended technical implementations are intentionally deferred to separate author-held materials, to maintain focus on testable structure rather than speculative extension. The framework is presented as ready to be constrained, refined, or rejected by forthcoming surveys such as Euclid (DR1+).