Classical and Quantum Gravity, and Oscillating Fingerprints: A Containment-First Discriminator on held a r↔r Magnitude Plateau

This release introduces the Oscillating Fingerprint: a mechanical, four-position geometry that separates Classical Gravity from a Quantum Gravity mediator on a held r↔r Magnitude plateau. The fingerprint arises by reading two weakly coupled mechanical modes (symmetric/antisymmetric) in two orthogonal quadratures (0°/90°), yielding a 2×2 observation grid. On this grid, a classical one-mode mediator collapses to rank-1 and produces a robust ~pi cross-phase step; a quantum two-quadrature mediator remains full-rank and shows no mandatory pi step. The work operationalizes a containment-first ladder (Consistency → Magnitude → Amplitude), mandates A/B hygiene freezes, and specifies a finite decision band with a numeric rank metric (s2/s1 thresholds) for pass/fail calls. It integrates positive Q fingerprints (e.g., entanglement witnesses, commutator-phase, state-dependent noise) that can be run on the same window, and includes translator-gate guidance (Up vs Down asymmetry) plus materials roles (Drude, strange metal, SC/dielectric). A minimal run card and decision tree convert the method into a lab-ready protocol. The Oscillating Fingerprint concept was first articulated in Quantum Vise and here becomes a concrete discriminator unifying the classical pi-step with quantum-compatible signatures.