Fibered Levels and Global Naturality in the Fractal Consistency Law

Fibered Levels and Global Naturality in the Fractal Consistency Law: Bifibration, adjoint scale maps, Beck--Chevalley coherence, path independence, and integrated hardening of multiscale coarse-graining Structural Foundations of the Fractal Consistency Law This paper presents the multiscale categorical sector of the Fractal Consistency Law (FCL) in a rebuilt and publication-oriented form. Its purpose is to show that the passage between microscopic and coarse-grained descriptions cannot be treated as an arbitrary averaging procedure, but must satisfy a global naturality condition if the theory is to possess a coherent effective sector. The paper formulates the scale architecture as a bifibration over a category of levels, introduces the adjoint pair relating refinement and coarse-graining, states the Beck--Chevalley coherence condition as the local elimination of route ambiguity, and derives the pseudofunctorial path-independence statement for the effective predictive sector. The already developed hardening is integrated directly into the body of the manuscript: route independence is defended as a physical admissibility criterion, not as a merely formal embellishment, and the distinction between admissible and arbitrary averaging maps is stated explicitly. Appendices collect the notation and the core coherence equations. The result is a coherent paper in which fibered levels, multiscale naturality, and path-independent prediction appear as a single structural module of the broader FCL program.