Newton's Cradle as Calibrated Impulse and Elastic-Mode Transfer: Momentum Conservation, Contact-Wave Propagation, Directional Constraint, and Resonance Unity in USP Field Theory (msf:52940 v1.0)

This document develops a calibrated description of Newton's cradle as a finite-duration mechanical transfer system within USP Field Theory. General momentum conservation, energy conservation, pendulum motion, elastic Hertzian contact, stress-wave propagation, normal modes, damping, and suspension geometry form the quantitative baseline. USP Field Theory contributes an operational interpretation in which the cradle passes through a loading–locking–release sequence: gravitational potential energy is loaded, impact temporarily locks energy into elastic contact geometry, and the stored energy is redistributed into directed output motion and secondary modes. The framework defines measurable impulse, contact time, directional transfer efficiency, transverse leakage, normalized elastic-energy density, modal response, and a dimensionless resonance-unity index (UR). It also introduces exact detector kernels for high-speed video, accelerometers, contact-force sensors, microphones, and strain gauges. A pre-excited receiving group is treated with a complete energy and phase ledger, allowing phase-sensitive reinforcement without violating energy conservation. Vacuum, material, alignment, and phase-scan protocols are provided, alongside strict statistical decision rules (such as ΔAIC) to test whether the USP coherence variables add transferable predictive value to classical models.