ACORN Booklet 14: Curvature Waves — Propagation Modes of the Curvature–Closure Framework

ACORN Framework Booklet Series The ACORN framework is a geometric curvature–closure approach to fundamental physics in which mass, quantisation, and dynamical behaviour arise from closed circulation of intrinsic curvature channels governed by a compact canonical operator structure. From these canonical relations emerge invariant closure norms, quantised loop actions, and universal recurrence relations organising stable physical structure. The ACORN booklet series develops the consequences of this canonical framework across multiple domains of physics. Each booklet begins from the frozen Canon and explores how familiar physical phenomena arise as projections or consequences of curvature closure dynamics. This booklet develops the concept of curvature waves within the ACORN framework. Curvature waves represent propagating disturbances of intrinsic curvature circulation that travel through the closure manifold while preserving the canonical invariants. These waves arise when local curvature configurations depart from equilibrium closure and redistribute curvature through the surrounding structure. Within this framework, electromagnetic radiation appears as a projected manifestation of such curvature waves, while other large-scale curvature modes may propagate without producing electromagnetic projection. These non-projecting modes provide a natural candidate for large-scale background curvature activity within the Universe. Curvature waves therefore provide a unified geometric description of radiative processes, propagation of dynamical curvature disturbances, and large-scale curvature oscillations that may manifest cosmologically. ACORN: Curvature Waves extends the closure framework by identifying the propagating modes through which curvature disturbances travel, linking local radiative phenomena with large-scale curvature dynamics across the same geometric structure.