Same Fingerprint, Different Physics: Pairing Systems by Odd-Null and Sign Flip with Falsification Testing

This note introduces a cross-domain method to pair seemingly unrelated physical systems by the same “Sigma-contrast” verdict: a tiny probe with odd/even demodulation that nulls the odd channel at the operating center (odd → 0) and flips sign under a mapped symmetry while the even channel remains invariant. We formalize four practical checks—G (center/plateau, R ≈ 1), Sigma (contrast quality), P (one-way process update with low backflow), and L (invariance/logging)—and combine them in a simple Pair Potential Score (PPS) to rank pairings on a 0–5 scale. Scope and expectations. This work does not claim hardware interoperability or identical timescales. “Work together” means two systems independently satisfy the same Sigma-contrast test within the operating envelope set by G, P, and L. If those gates are violated (poor phasing, drifting center, backflow, or permutation sensitivity), the pairing should fail—by design—providing a falsifiable boundary. Two anchor pairs (RF phase-locked loop vs microwave cavity reflection lock; optical OAM cavity vs Fabry–Perot lock) calibrate the scale. The same acceptance lines extend across graphene QHE and YIG magnons, spin Hall and Floquet drives, microring Kerr combs and NV ODMR, topological photonics, power-core phenomena (Barkhausen/Shapiro; Metglas), and microfluidic diodes. For reproducibility, we include a falsifiability protocol (blinded sign test, angle hygiene, no-spoof plumbing controls, small-signal scaling, and permutation invariance) and quick triage tables that identify the most likely gate to fail and the fastest mitigation. Minimal logs (flip state, odd/even channels, probe/lock-in settings) are sufficient for independent confirmation or refutation on any bench.