Closure of Physical Theories from Suppression, Coherence, and Fixed-Point Selection

Theory-agnostic constraints on physically admissible theories are derived from four minimal requirements: (i) existence of observable records, (ii) finiteness of information per finite region, (iii) local compositional propagation, and (iv) persistence of macroscopic causal coherence. Three coupled pillars follow: (a) a universal suppression bound stating that influence on record observables decays at least exponentially with causal depth, (b) a bulk–boundary coherence inequality bounding the rate of distinguishable bulk novelty by the rate of record formation after compression, and (c) an observability fixed-point principle stating that persistent observable universes require equilibria in which suppression and bulk novelty are jointly balanced under coarse-graining. These results imply a closure theorem: every degree of freedom is either constrained by finite-depth observability conditions or becomes physically irrelevant via suppression at unbounded depth. Closure constraints propagate bidirectionally across scales, and may also act as a consistency filter on pre-existing microscopic dynamics when exponential suppression is intrinsic to the underlying amplitude or weight structure. Universal failure modes—over-suppression, coherence violation (overload), and absence of admissible fixed points—are classified. No new dynamical fields are introduced and no modified equations of motion are assumed; the results are necessary conditions for persistent observability in any causal physical theory.