Alignment as Gradient Consistency in Multi-Agent Systems

This paper analyzes alignment as a problem of multiscale dynamical consistency rather than value specification. Building on a bounded completeness framework, we distinguish local structural descent—defining intelligence—from global descent—defining normative stability. We show that these two conditions are logically independent: locally descending agents may collectively induce ascent in a global completeness functional. We formalize alignment as gradient coherence between local and global completeness functionals. The central result provides a necessary and sufficient condition under which local descent implies global descent: the induced collective displacement must lie within the descent cone of the global functional. Alignment is thereby characterized as a compatibility condition between Lyapunov structures in a coupled dynamical system. The analysis reframes alignment without appeal to externally specified objective functions. Instead, it identifies a geometric constraint required for truth-oriented refinement to remain collectively coherent. From this, a minimal form of structural normativity emerges as preservation of multiscale descent relative to an ontic embedding. The result clarifies the relation between rational agency, collective stability, and truth-directed dynamics across biological, social, and artificial systems.