Emergent Rung Model Space: A Constrained Framework for Scale-Recursive Dynamics

Emergent Rung Model Space is a restrictive framework for exploring scale-recursive models in which the observed universe is treated as one instance within an infinite hierarchy of scale intervals, related by exact repetition rather than qualitative variation. The framework is defined to exclude unconstrained recursion: structure, admissible dynamics, and patterns of interaction are required to be invariant across repeated scale intervals, not merely analogous.

The framework enforces two non-negotiable constraints. First, directly inaccessible scale intervals must be internally indistinguishable from the observable one when described in their own native units: the same classes of degrees of freedom, admissible dynamics, and effective organization must recur, differing only by a fixed rescaling of space and time. Second, coupling between neighboring scale intervals is mandatory and invariant: the form of inter-scale interaction may not depend on position in the hierarchy, and it must impose non-trivial, in-principle testable constraints on observable physics.

These requirements sharply limit the allowed model space. They forbid isolated hidden sectors, terminal ultraviolet or infrared cutoffs, and recursive constructions in which additional scales host qualitatively different behavior or interact in scale-dependent ways. Empirical agreement with established effective theories is necessary but not sufficient for framework applicability; a universe in which all observable phenomena are demonstrably closed under all admissible interpretations admits no realizations.

Emergent Rung Model Space is not a theory of fundamental physics but a constrained search space for model construction. If the space it defines is empty, that emptiness is itself informative. If it is not, the framework identifies a narrowly defined setting in which scale recursion is both structurally rigid and empirically constrained, making it a focused target for technical investigation rather than an open-ended speculation.