The Law of Predictive Coherence (LPC): A Memory–Tension Stability Condition for Distributed Predictive Systems

We formulate the Law of Predictive Coherence (LPC) as a stability condition for distributed predictive systems. The law is centered on the inequality τ(t) ≤ f(M(t)), where τ(t) denotes predictive tension and M(t) adaptive memory. In this view, stability is achieved not by fixed equilibrium alone, but by maintaining predictive divergence within the range supported by accumulated coherence. We define predictive tension through a divergence measure, model adaptive memory through a decaying coherence kernel, and introduce a minimal dynamical system coupling tension relaxation and memory accumulation. For multi-agent predictive systems, we complement this picture with resonance-based network coupling, a Laplacian coherence proxy, and diversity-preserving adaptive weights. The contribution of this note is not to propose a universal final framework for all physical, informational, and cognitive systems, but to state a compact phenomenological law with explicit observables and falsifiable consequences. In the present version, empirical illustrations are treated as supportive rather than constitutive of the claim.