The Breathing Universe: 211_Relativity as Zero-Line Dynamics

The Breathing Universe: Relativity as Zero-Line Dynamics develops a structural reconstruction of relativistic physics within the broader Breathing Universe Model (BUM). The work places relativity inside a typed architecture extending from foundational admissibility and primordial balance through structural differentiation, realization, coherence, persistence, emergent geometry and physical time, spacetime, effective physics, projection, and observation. The reduced relativistic sector is treated as a downstream representation of an already-realized physical regime rather than as the foundational ontology itself. The central construction introduces an effective persistence–transport relation, P² + T² = P₀², together with T/P₀ = v/c and P/P₀ = Δξ(v)/Δξ₀. These assumptions yield Δξ(v) = Δξ₀√(1 − v²/c²) and therefore recover the standard Lorentz factor exactly as γ = Δξ₀/Δξ(v) = P₀/P = 1/√(1 − v²/c²). With the additional standard inertial-frame assumptions of linearity, spacetime homogeneity, spatial isotropy, reciprocity, and invariant local null propagation, the ordinary Lorentz transformations and associated Special-Relativistic relations are recovered. The result is therefore presented as a conditional structural recovery of Special Relativity, not as a first-principles derivation of Lorentz symmetry from the complete BUM architecture. The paper further distinguishes massive kinematic Zero-Line proximity from the photon-like null sector and separates local propagation from global causal accessibility. This Propagation–Accessibility Separation Principle allows invariant local light propagation at c to coexist with vanishing observer-relative accessibility at gravitational or cosmological horizons. General Relativity is treated through an effective Einsteinian correspondence regime, while the microscopic structural-to-metric map from persistent realized structure to gμν remains an open derivational problem. Unified Energetics is incorporated using the disambiguated effective quantity H_E, with the mass-linked invariant relation E₀ = H_EΩ, m = H_EΩ/c², and hence E₀ = mc², while moving massive states obey E = γE₀. The work also clarifies the distinct roles of realization, coherence, persistence, geometry, accessibility, projection, and observation, and explicitly separates formalization, derivation, phenomenological parameterization, prediction, and empirical confirmation. The paper does not claim complete predictive closure. Instead, it identifies the remaining requirements for such closure, including derivation of the persistence–transport relation, emergence of the invariant propagation scale, microscopic metric generation, matter coupling, energetic foundations, cosmological dynamics, and quantitatively discriminating observational predictions.