SDC v1.6.1: A Phenomenological Observable Bridge with Explicit Correspondence and Falsifiability

We present SDC v1. 6. 1, a minimal phenomenological framework that defines a structurally consistent mapping from an abstract differentiation field C (x, t) to observable cosmological quantities, including H (z), q (z), wₑff (z), and fσ8. This work is intentionally minimal: its purpose is to define a structurally consistent and testable bridge between abstract differentiation dynamics and observable cosmology. The construction enforces a correspondence principle: in the limit of low structural contrast and slow variation, the model reduces to an effective ΛCDM-like description, ensuring continuity with established observations. Beyond this regime, SDC predicts systematic, scale-dependent deviations that define a distinctive observational signature. The framework is not yet a full first-principles theory. It does not include a fundamental action, complete perturbation theory, or full CMB and nonlinear N-body predictions. Instead, it serves as a constrained observable mapping designed to isolate falsifiable consequences. A falsifiability matrix is explicitly provided, specifying conditions under which the model can be weakened or rejected by data across geometry, growth, and joint probe consistency. All accompanying code is intentionally minimal and serves only to demonstrate the internal structural mapping and its observable consequences, not to provide a full numerical validation. The central claim of this work is therefore not completeness, but testability: SDC defines a minimal bridge between structure and observation while providing distinct predictions that can be directly confronted with future high-precision data.