Coherence, Perturbation, and Recovery in Large-Scale Structure: A Relational Framework for Interpreting Cosmological Stability

Large-scale cosmic structure formation is commonly interpreted through perturbation growth, effective field theories, and statistical inference frameworks that characterize how matter distributions evolve under expansion. While these approaches successfully model structure emergence and redistribution, they offer more limited conceptual tools for explicitly tracking coherence: the persistence, degradation, or loss of relational structure under sustained perturbation. This paper examines the applicability of the Dynamic Fractal Theorem of Relation (DFTR)—a general framework developed to describe coherence dynamics across complex systems—to the interpretation of large-scale cosmological structure, particularly in the context of Euclid-scale observations. Rather than proposing a new cosmological model or modifying ΛCDM, the analysis explores whether DFTR’s core distinctions between perturbation, reorganization, and viability constraints provide interpretive value for understanding structural persistence and failure modes in cosmology. Within this framework, reorganization is treated as conditionally stabilizing rather than inherently beneficial, allowing for regimes in which increased corrective activity accelerates incoherence rather than recovery. A minimal relational dynamical representation is introduced to constrain coherence trajectories without prescribing domain-specific mechanisms or parameters. The framework is applied as an interpretive lens to Euclid-relevant observables such as weak gravitational lensing and large-scale clustering, highlighting how coherence loss may occur even when standard stability or correction metrics appear well behaved. By positioning DFTR as a transferable interpretive framework rather than a cosmology-native theory, this work aims to clarify when and why structural persistence succeeds, degrades, or fails under sustained perturbation, and to outline conditions under which future Euclid analyses could meaningfully test the relevance of coherence-based interpretations.