HDC-CBC/Ib Structural Classification of Physically Admissible Correlations

Abstract

We present HDC–CBC/Ib, a Supplementary Structural & Interpretative Program (SSIP) integrated within the framework of the Hypothesis of Correlational Disequilibrium and the Correlated Bubble-Cosmos (HDC–CBC / CBCₜ). This work does not introduce new dynamics, degrees of freedom, or additional physical parameters. Its aim is to determine, from the internal logic of the formalism itself, which types of correlation may be considered physically admissible and which cannot be stabilized as emergent regimes.

The starting point is the central correlational variational principle of the framework,

interpreted here not as an equation of motion, but as a structural condition of existence. From this reading, minimal criteria of structural stability, persistence under coarse-graining, and effective projectability are formulated, making it possible to discriminate explicitly between mathematically conceivable correlations and correlations capable of sustaining observable physics.

On this basis, a systematic typology of correlations is developed, organized through structural quadrants, in which non-admissible correlations, transient correlations, structurally admissible correlations, and correlations associated with regime transitions are distinguished. The analysis shows that only a strongly restricted subset — structurally admissible correlations — can emerge as a physical regime, while most correlational configurations are excluded because of instability, lack of persistence, or excessive microscopic dependence.

In this context, notions such as geometry, temporality, locality, and cosmology are not introduced as fundamental categories, but as effective projections of stabilized correlations, valid only within finite regime domains. Geometric and cosmological emergence are thus interpreted as regime-dependent phenomena, compatible with the existence of a non-projected basal state (Greater Cosmos) and consistent with the interpretative equivalence ER = ERP established previously.

Finally, we show through a minimal structural example that HDC–CBC possesses internal discriminative power, thereby avoiding retrospective immunization and preserving the indirect falsifiability of the framework. HDC–CBC/Ib thus completes the initial block of the SSIP program and consolidates the conceptual architecture of the model without modifying its ontology, its dynamics, or its predictive content.