Structural Cosmology v3.0: A Core Theory of Structural Differentiation and Cosmic Structure

Structural Cosmology v3.0 presents a unified theoretical framework for interpreting cosmological evolution through the five-stage meta-ontological sequence I → D → S → A → F (Isness, Difference, Structure, Appearance, Feedback). The framework proposes that a single real scalar structural field Δ(x,t), governed by an effective potential V(Δ) and dynamic friction Z(Δ), can provide a unified interpretation of both dark energy-like cosmic acceleration and dark matter-like structure formation. Building upon the phenomenological, field-theoretic, perturbative, and nonlinear developments introduced in previous versions, v3.0 integrates these components into a single coherent core theory. The theory introduces a closed-loop architecture linking field dynamics, projection operators, observational observables, and iterative refinement through the Data-Guided Refinement (DGR) and Generative Growth of Predictive Theory (GGPT) framework. Observable quantities are interpreted as projections of the underlying structural field through a generalized projection operator Πg, enabling cross-observable consistency tests across cosmological probes. A unified falsifiability network of 40 complementary tests (C1–C40) spanning cosmic expansion, large-scale structure, weak lensing, CMB physics, velocity fields, compact objects, and fundamental physics is defined. The framework is presented as an exploratory and illustrative research programme, employing reviewer-safe scientific language throughout. Key testable signatures include geometry-growth decoupling, scale-dependent effective gravitational coupling G_eff(k,z), projection-based consistency relations, and future observational comparisons with Euclid and other multi-probe surveys. This release represents the first unified core-theory formulation of Structural Cosmology, integrating the complete v1.x–v2.3 development programme into a single theoretical architecture.