From Physical Limit to Sustainable Civilizational Load — Current State of the Derivation of k

This preprint presents the current state of a derivational attempt within the Consciousness of the Real (CdR) framework: the extension of the structural law rho · C ≈ k from the physical domain to the civilizational domain. The document does not claim that the derivation is fully closed. Instead, it distinguishes carefully between what is now structurally established and what remains theoretically open. The following points are treated as established: the structural traceability of the sequence image004 → image008 → image009 → kciv; a non-circular candidate definition of active civilizational axes; the use of coupling matrices to represent inter-axis dependency; the derivation in candidate form of buffering and compositional terms from the existing corpus; an explicit rule of passage between ontological quantities and proxy-scale measurements. The main open problem is also stated explicitly: the exact functional relationship between hierarchical compositional depth and coupling topology in a civilizational network. The current derivation is therefore presented as largely structured, but not yet numerically complete. The note is intended as a research-state document: not a final demonstration, but a constrained and critical consolidation of what has been achieved so far, and of the precise theoretical bridge still required. This record includes English and French versions of the document. Author: Sylvain LebelWith editorial assistance from ChatGPT and critical review by Claude.