The Breathing Universe: 712_Complementary Asymptotic Resolution and Causal Accessibility

Abstract The Breathing Universe Model (BUM) describes physical reality as an emergent coherence architecture organized around complementary tendencies of localization and delocalization and referenced to a fundamental balance condition, the Zero-Line. This paper unifies several previously separated elements of the framework: asymptotic large-scale evolution toward balance, persistence and intensification of localized coherent structure, horizon-regulated vacuum curvature, relativistic Zero-Line proximity, invariant geometric propagation, black-hole accessibility boundaries, and the long-time causal structure of the universe. A central result is that global flattening and local intensification are not contradictory. The global structural deviation may approach balance, Delta xi_G -> 0, while localized coherence and gravitational concentration remain finite or temporarily increase. Global balance therefore does not require local erasure. The paper distinguishes the effective infrared coherence scale R_coh from the Hubble radius, particle horizon, and future event horizon. The horizon-regulated vacuum relation is written as Lambda_BUM = xi_H / R_coh^2. Future causal reach is determined independently by chi_fut(t) = integral from t to infinity of c dt'/a(t'). Consequently, H_c -> 0, Lambda_BUM -> 0, or even R_event -> infinity does not by itself imply disappearance of the future event horizon; the asymptotic integrability of 1/a(t) is decisive. The geometric BUM limit conventionally written as H -> c^2 is reinterpreted as entry into an Invariant Geometric Propagation State, G_c, with H^(geom) -> c^2 and v_prop -> c. This geometric limit is distinguished from the balance-sector limit H^(bal) -> 0. The two represent different effective projections of the underlying redistribution architecture rather than contradictory limits. A Propagation-Accessibility Separation Principle is introduced. Near a black-hole event horizon, local propagation may remain relativistic, v_local = c, while causal accessibility and projection satisfy A_acc -> 0 and Pi -> 0. The horizon is therefore interpreted as accessibility closure rather than local propagation collapse. The paper further develops a dynamical closure program connecting (Delta xi_G, Omega_G) -> R_coh -> Lambda_BUM -> H_c -> a(t) -> chi_fut. Several asymptotic causal branches are classified. A particularly significant possibility combines global causal opening with persistent local causal closure: the cosmological future event horizon may be absent while black-hole horizons remain as local accessibility boundaries. The global out-breath and local in-breath are thereby interpreted as complementary redistribution channels within an asymptotically balancing realized universe. Keywords Breathing Universe Model; Zero-Line; asymptotic resolution; global flattening; local intensification; localization; delocalization; causal accessibility; future causal reach; event horizon; cosmological horizon; black holes; horizon regulation; infrared coherence scale; invariant propagation; speed of light; geometric propagation state; vacuum tension; vacuum energy; structural differentiation; coherence; projection; conformal time; emergent relativity; dynamical closure; asymptotic cosmology