Auto-Organized Dissipative Structures and Regularity on Global Attractors: An Onsager–Cheeger–Renormalization Framework

We propose an axiomatic multiscale framework for dissipative dynamical systems with aglobal attractor, organized around a single principle:nonnegative Onsager production propagates under coarse-graining.At a fixed observation scale, each interface carries a sum-of-squares Onsager–Prigogineproduction polynomial, hence matrix/scalar Onsager bounds and a canonical misalignmentdefect. Eliminating intermediate scales by minimum-production decimation preserves thisstructure and defines an autonomous renormalization map on shell graphs. Fixed points ofthis map are precisely configurations that satisfy Prigogine closure at all scales simultaneously.On the same observed graph, the production structure induces a weighted Dirichlet formand a Cheeger-type dichotomy: either the scale–channel graph is coercive (self-averaging andreverse-Hölder improvement) or bottlenecked (flux suppression and tail drainage). Combinedwith an observationwise entropy-transport package and an explicit modular coercive-closureinterface, both branches yield regularity upgrades on the global attractor. At the renormalizationlevel, hyperbolic saddles organize transitions between universality classes: shadowtimes, parameter accumulation, and finite-size corrections are controlled by the unstable RGeigenvalue δu, while the closed thermodynamic sector carries its own explicit dyadic drifteigenvalue δth = 2.The manuscript is intentionally modular. We state explicit axioms (A0, A0♭, A0♯, A1–A6), prove the abstract implications conditional on those axioms, and separate them frommodel-dependent verification programs. In particular, no new well-posedness theorem for 3DNavier–Stokes is claimed here. A companion numerical campaign on Sabra and GOY shellmodels validates several theorem-level diagnostics of the thermodynamic RG (Appendix L)and keeps all phenomenology-level and transition-dynamics items explicitly non-claim.