TSR-Q-1: A Preregistered Experimental Protocol for Testing Structured Quantum-Coherence Residuals in Superconducting Qubits

TSR-Q-1 presents a preregistered and falsifiable experimental protocol designed to test for structured late-time coherence residuals in superconducting transmon qubits. The protocol does not treat generic recoherence, non-exponential decay, or non-Markovian behavior as evidence for the proposed framework, since such phenomena may arise from conventional open-system mechanisms. Instead, it targets a specific normalized temporal scaling law, tₙ/T₂ = nᵏ, with the preregistered theoretical value k* = 1.4706, corresponding to the first two target locations t₂/T₂ = 2.7714 and t₃/T₂ = 5.0310. If the associated amplitude-scaling hypothesis is retained, the predicted ratio is A₃/A₂ ≈ 0.551. The accompanying computational validation package develops the analysis pipeline through five stages: preliminary signal injection, blind null testing, blind injection-recovery, multi-qubit global-k inference, and sensitivity mapping. The synthetic null models include stretched-exponential decay, 1/f^α correlated noise, random-telegraph/TLS-like contributions, slow drift, white noise, and device-to-device variability. These simulations validate the detectability, specificity, and sensitivity of the proposed analysis procedure under the tested synthetic noise families. They do not constitute experimental evidence for the existence of the predicted physical effect. The next stage is a preregistered hardware implementation using superconducting qubits, with device-specific null calibration, blind analysis, systematic controls, held-out replication, and, ultimately, independent experimental replication.