The Breathing Universe_901 Post-Snap Coherence Persistence and Emergent Dark-Sector Geometry

This paper develops a persistence-based cosmological framework within the broader Breathing Universe Model (BUM), formulated as an exploratory effective field theory (EFT) of coherence-supported organization, synchronization dynamics, transport structure, and emergent curvature reconstruction. The framework introduces generalized coherence participation fields, synchronization sectors, transport tensors, environmental stabilization structure, and projection-dependent observability operators as interacting components contributing collectively to effective gravitational sourcing. Within this approach, galactic rotation curves, weak-lensing phenomenology, cluster-scale organization, filamentary continuity, and large-scale structure growth may emerge from distributed coherence-supported persistence structure rather than solely from compact particulate dark matter halos. The paper derives generalized effective stress–energy sectors, perturbative growth equations, halo equations, lensing relations, synchronization dynamics, and anisotropic transport structure within a unified EFT formalism. Particular emphasis is placed on coarse-graining behavior and the recovery of effective ΛCDM phenomenology at large scales, while simultaneously allowing for potentially observable residual structures beyond standard reconstruction limits. These residuals may include environmental halo dependence, filament-aligned weak-lensing asymmetries, synchronization-sensitive morphology, shell-transition signatures, transport-induced anisotropies, and projection-dependent observational effects. The work further develops stability conditions, renormalization structure, EFT validity limits, perturbative closure requirements, numerical roadmaps, and observational validation programs. Extensive appendices formalize the mathematical notation, lensing estimates, halo phenomenology, EFT extensions, ontological interpretation, and relation to earlier BUM papers. The framework is not presented as a completed microscopic theory or UV-complete description of nature. Instead, it is proposed as a mathematically structured exploratory persistence-based alternative to conventional dark-sector interpretation, whose scientific viability depends on whether observationally distinguishable residual structures survive beyond the coarse-grained ΛCDM recovery limit.