The UV-IR Bridge in Gravity: A Self-Consistent, Resolution-Dependent Backreaction and Interscale-Descent Framework

The UV-IR Bridge in Gravity: A Self-Consistent, Resolution-Dependent Backreaction and Interscale-Descent Framework (v1.1 )addresses the apparent scale tension between gravity's microscopic weakness in quantum processes and its macroscopic dominance in astronomical systems. Rather than treating these behaviors as consequences of a single scaling parameter, this preprint places them within a common, resolution-dependent architecture. The framework formalizes this connection through a self-consistent coarse-graining and backreaction equation, \mathcal{F}_L[g, \rho] = 0, which maps microscopic quantum states to an effective geometric response. This paper introduces a falsifiable diagnostic methodology for evaluating effective geometric models, featuring: Coupled Admissibility Conditions: Four pointwise "locks"—EFT control, covariant source, stability, and fidelity—that are combined into a joint defect function to diagnose when a classical or stochastic geometry is a valid representation at a given scale. The Fifth Failure Mode: The framework demonstrates that pointwise admissibility at two different scales is insufficient to guarantee a genuine physical connection; a true bridge requires a directed, composable interscale map. Failure of this descent is defined as the fifth, intrinsically multiscale failure mode. Interscale Obstruction and Repair: By deriving a "Two-State Witness Lemma," the paper proves that descent must be tested uniformly over a declared state family, yielding a sharp lower bound on the resulting obstruction. It then introduces a "target-relative closure residue" to mathematically repair the broken bridge by adjoining specific discarded relational information. As part of the Kruse Continuum series, this work explicitly bypasses the attempt to derive classical spacetime from a complete fundamental theory of quantum gravity. Instead, it provides a structured method for determining when an effective geometric description is genuinely descended from finer scales, rendering theoretical failures as measurable, diagnostic features.