ECF IV: The Principle of Correlation Extrema — The Triple Convergence of Mathematics, Physics, and Information

Version: Version 4.0 (new version; the concept DOI chain is preserved) Version description: This updated version contains the information-concept reconstruction of the preceding version — the coupling consistency \\(C\\) (a quantity of the two-face relation, normalized to \\([0,1]\\)) and the metric-face encoding capacity \\(I_M\\) (an auxiliary spectral quantity) are separated, and the unified functional is \\(\\Omega = S + 1/C\\) — and adds: the full adoption of the generative-framework language (generation nodes, generation paths, fully generated; the caveat removed); the configuration hypothesis and Assumption (A2) aligned with ECF III §4.2 (differentiable with strictly signed derivatives); the kernel symmetry marked as a C-tier construct choice; the Hadamard bound restricted to the full-rank case; Part II restated as a structural B/C generation path; the self-reference DOI placeholder replaced by the real DOI; and the abstract wording unified with the qualitative-maximum statement of the theorem.