A Multiscale Wavefunctional-to-Geometry Bridge in Canonical Quantum Gravity: Fractal Decomposition, χ-Stabilized Flow, and Collapse/Blow-Up Regulation

A central challenge in canonical quantum gravity is not only the frozen structure of the Wheeler–DeWitt constraint, but the absence of a practical and stable map from a wavefunctional over geometries to an effective classical geometry with sustained evolution. This paper proposes a multiscale “wavefunctional-to-geometry bridge” in which the quantum state is decomposed into a scale-cascade representation (a fractal/wavelet expansion), and an effective geometry is read out as a functional of multiscale energy and phase structure. A flow rule is introduced by extending the Wheeler–DeWitt constraint with an explicit scalar time field, yielding intrinsic evolution across the multiscale cascade. The Chronos stability constant χ is used as a dimensionless regulator that maintains bounded evolution by preventing collapse (over-diffusion) and blow-up (over-coupling) in the scale hierarchy. The framework is formulated explicitly and illustrated with a toy model demonstrating three regimes: collapse, blow-up, and χ-stabilized sustained geometric flow.