Structural Cosmology v3.2 develops a Cross-Scale Consistency framework extending the Structural Cosmology programme established in v3.0 and v3.1. Within this framework, all observable quantities are interpreted as projections of a common structural field Δ(x,t) through scale-dependent projection operators ΠgX(k,z). Cross-scale consistency is proposed as a non-trivial and testable property of the framework, requiring observables derived from the same underlying structural field to exhibit mutual coherence across scales, redshifts, probes, and messengers. The work introduces a three-layer scale hierarchy (Microscopic, Mesoscopic, and Macroscopic) and develops illustrative consistency conditions associated with causality, screening, halo dynamics, cosmic expansion, growth of structure, redshift evolution, and cross-probe agreement. Several quantitative consistency diagnostics are presented, including the EG statistic, CMB–LSS cross-correlations, BAO consistency relations, and a geometry–growth decoupling test. A cross-scale consistency index and a DGR/GGPT-based feedback pipeline are proposed as illustrative tools for model evaluation and refinement. The framework further extends the falsifiability network of Structural Cosmology from C1–C45 to C1–C50 through five new consistency-oriented tests addressing geometry, growth, structure, redshift evolution, and cross-probe compatibility. Survey-scale applications involving Euclid, Rubin/LSST, SKA, LISA, and CMB-S4 are discussed, together with a roadmap toward future developments of the Structural Cosmology programme. All results are presented as illustrative and exploratory. Consistency across probes is expected within the framework but is not guaranteed a priori; significant and persistent inconsistencies would challenge the framework.
Koji Okino (Sat,) studied this question.