Scale-Invariant Geometric Threshold for Macroscopic Quantum Coherence: Deriving the Exact Superconducting Phase Collapse Limit via Spatial Propagation Dynamics

The prediction of the critical temperature (Tc) in high-temperature superconductors (HTSC) remains a foundational challenge in condensed matter physics, frequently defying standard BCS weak-coupling approximations. Current phenomenological models, like Ginzburg-Landau theory, effectively describe the behavior of the superconducting state but fail to provide a deterministic, parameter-free calculation for the precise moment of phase coherence collapse. This paper introduces a non-statistical, deterministic topo-dynamical framework for macroscopic quantum coherence. By modeling the phase-locking propagation of Cooper pairs as a continuous spatial expansion operator competing against the localized structural decay of thermal phonon scattering, we derive a scale-invariant geometric threshold (Λ∗). We mathematically demonstrate that this invariant maps directly to the critical coherence length ξc. By integrating this limit into reel-to-reel manufacturing feedback loops, we outline a generalized, parameter-free methodology for engineering maximum-stability superconducting tapes with deterministically defined critical phase boundaries.