RDCC–Euclid Interface (v50.0)

Summary This paper delivers the survey-ready cosmological interface for **Relaxation-Driven Cyclic Cosmology (RDCC v50.0)** tailored for the upcoming **ESA Euclid DR1** and future data releases. By enforcing a strictly null-like primordial Maxwell boundary state ($F^2 = 0$), the inter-sector interaction space collapses from a multi-fluid phenomenology into a **single effective vacuum-relaxation axis ($w_{\text{int}} = -1$)**. Core Features & Euclid Observables Instead of tracing a standard clustering dark matter particle, this framework models deviations from $\Lambda$CDM as a pure geometric vacuum response, creating a highly constrained pattern of cross-probes: * **Growth & Lensing:** Predicts correlated, scale-dependent growth suppression ($f\sigma_8$) and broad cosmic shear restructuring ($P_\kappa$). * **Gravitational Slip:** Evaluates the spatial transition scale between the metric potentials $\Phi$ and $\Psi$. * **Non-Gaussian Geometry & Topology:** Maps the vacuum axis directly onto higher-order field statistics, using **Minkowski Functionals** for map morphology and **Persistent Homology** ($W_2$ optimal-transport metrics) for cosmic web topology. The RDCC Consistency Relation The defining feature of this framework is a strict, parameter-free topological consistency condition: $$\alpha_{\text{growth}} \simeq \alpha_{\text{lensing}} \simeq \alpha_{\text{geometry}} \simeq \alpha_{\text{topological}}$$ A successful joint fit requires that a single relational coordinate $\alpha(t)$—measuring the fractional displacement from the CPT-symmetric bounce configuration—simultaneously accounts for all observational sectors.