HDC-CBC/Δ Dynamic Rupture of Correlational Equilibrium

In this work, the stability of the basal correlational state (Greater Cosmos) is analyzed within the HDC–CBC framework (Hypothesis of Correlational Disequilibrium and Correlated Bubble-Cosmos), attending exclusively to its own variational principle. In the pre-geometric limit, where no projected geometric sector exists, the general principle reduces to the condition identifying the basal state as a critical point of the correlational functional. A minimal formalism is constructed in a one-dimensional state space, without introducing spacetime structure, fundamental temporal parameters, or new dynamical degrees of freedom. Under a strictly dissipative gradient-relaxation scheme, it is shown that the stability of the basal state depends only on the sign of the local second variation The stable, marginal, and unstable cases are distinguished, and it is argued that the structural compatibility between maximal correlational coherence, non-trivial relaxation, and absence of external mechanisms favors the scenario in which the Greater Cosmos corresponds to a local variational maximum. Under this condition, any physically admissible correlational deviation induces a monotonic descent of basal energy and necessarily generates a projectable regime with increasing effective scale. The emergence of scale is not postulated as an additional hypothesis, but is derived from the very relaxation dynamics of the correlational functional. The conditions of global stability of the functional, the need for lower boundedness to avoid non-physical divergences, and the structural robustness of the mechanism under smooth deformations are also analyzed. Finally, the indirect falsifiability of the proposed scenario is discussed, pointing out that the absence of critical thresholds, abrupt transition signatures, and primordial oscillatory behavior constitutes a structural consequence of the model. The result establishes the dynamical bridge between the unprojected Greater Cosmos and the geometric regime developed in volumes Ω and related works, showing that the emergence of the projected universe is not contingent nor dependent on an external trigger, but rather a necessary consequence of the correlational principle itself under minimal and explicit hypotheses.