Wavefunction-to-Stationary Oscillation Bridge: An Operational Mapping for the Electron in USP Field Theory (msf:48121 — Canonical Upgrade of msf:48120)

This document presents a rigorous operational bridge between standard quantum mechanics (QM) and the ontological framework of USP Field Theory (USP). Quantum mechanics predicts electron behavior using the wavefunction ψ(r,t). USP Field Theory proposes a physical interpretation: the electron is a spatially extended, stationary oscillation stabilized within detuning corridors defined by the field parameter Δf(r). This work does not modify the Schrödinger equation, the Born rule, or any experimentally verified quantum predictions. Instead, it provides a translation layer between: QM predictive formalism and USP geometric oscillatory ontology. The bridge is constructed through four key elements: Explicit Born–Energy Mapping The probability density |ψ(r)|² is mapped to a physical stationary corridor energy density: u(r) = κ |ψ(r)|² where κ is fixed by normalization so that the integrated energy equals the magnitude of the bound-state energy. Time-Dependent Detector Coupling Model Measurement is modeled as localized energy exchange between the stationary mode and a detector kernel: dE_det/dt = γ_det ∫ u(r,t) K(r − r0) d³r The Born profile emerges in the sharp-kernel limit. Worked Hydrogen 1s Example The hydrogen ground state is used to demonstrate explicitly how the convolution with a Gaussian detector kernel reproduces standard detection probabilities. Minimal Falsification Protocols The document provides experimentally testable predictions involving: – Detector kernel width sweep – Controlled coupling strength and bandwidth – Coherence lifetime versus transport length msf:48121 operationalizes the ontology proposed in msf:48120, converting a conceptual interpretation into a mathematically structured, experimentally framed bridge. The wavefunction remains the correct predictive object. USP supplies the physical interpretation of what exists between interactions.