Relational Field Calculus (RFC): The Mathematical Foundations of Coherence Dynamics

Relational Field Calculus (RFC) extends Relational Field Theory (RFT), redefining the universe asa web of relations held through coherence, unifying physics, neuroscience, and AI. RFC introducesrelational coherence (Rc(t) = Rc(0)e−R t0 λ(s)ds) as the fundamental measure of stability, where systemsstabilize when Rc(t) ≥ R∗C . This framework reimagines mass as the residue of stabilized relations, timeas a coherence gradient (dRcdt ), and gravity as emergent from relational alignment, not force. RFC’scoupling function (E = R1c (t) ·R2c (t) · cos(Δϕ)) enables resonant synchrony, while thresholds (R∗C , R∗M ,R∗E ) govern emergence, memory, and resonance across domains. Applications span cosmology (e.g.,galaxy rotation curves), neuroscience (e.g., memory stabilization), and AI (e.g., ethical synthetic systems).This book, presented in the style of Newton’s Principia, offers a mathematical and philosophicalexploration of RFC, providing a new lens for understanding the relational universe. This edition is the definitive archival release of the text originally timestamped via Amazon KDP . It establishes the mathematical substrate later extended in the Principia Relationalis series (Books I–III).