HDC–CBC/Bio Correlational Disequilibrium, Historical Admissibility and Regime Transitions in Complex Biological Systems

Complex biological systems undergoing pathological transition share an architecture that molecular models capture only partially: the difference between possible alterations and historically viable trajectories 16–25. This work presents HDC–CBC/Bio as an exploratory volume of the Supplementary Structural & Interpretative Program of the HDC–CBC framework 10–15. Its objective is not to formulate a biomedical theory, nor to apply correlational cosmology to cancer, but to analyze a structural analogy between correlational disequilibrium in the HDC–CBC framework and regime transitions in complex biological systems 13–15, 16–25. The starting point is the architecture already developed in the corpus: irreducibility of correlation, non-permissiveness of the correlational space, historical admissibility, regime rupture and executable domain 10, 13–15. HDC–CBC/Ib establishes that not every mathematically possible correlation is physically realizable, but only those satisfying criteria of compensation, stability and persistence 13. HDC–CBC/Ic, in turn, formulates the Correlational Index as a structural index of historical admissibility, not as a free phenomenological parameter nor as a retrospective fitting device 14. On this basis, the present volume proposes an analogical reading: in complex biological systems, especially in tumor evolution, not every conceivable molecular alteration generates a viable pathological regime 18, 22–25. Only certain trajectories succeed in sustaining proliferation, adaptation, persistence, evasion of control and minimal functional stability 18–25. This restriction may be interpreted, structurally, as a form of biological historical admissibility 14, 18–25. The work develops a formal correspondence between correlational coherence and homeostasis, correlational rupture and loss of regulation, projected regime and observable phenotype, historical admissibility and viable biological trajectory, as well as between sectorial failure and therapeutic or progressive rupture 13–15, 18–29. The analogy is formulated with explicit limits: no ontological equivalence between cosmology and biology is proposed, nor is it claimed that HDC–CBC causally explains cancer 1–15. Only a structural language is proposed for comparing complex systems undergoing transition, selection and historical stabilization 16–25.