Version 1.3 revised preprint. This version refines the manuscript’s scope and framing, strengthens the error-analysis section, adds conflict-of-interest and data-availability statements, and aligns the paper more explicitly around the observational claim of carrier-period invariance within the detectable envelope. This preprint documents the measured carrier period (Tc)(T_c)(Tc) in a coupled system of repelling magnetic pendula within the Active Magnetic Cradle (AMC) configuration, using Case Study 3 as the focal dataset. It presents the experimental setup, Tracker-based motion analysis workflow, peak-detection method, histogram results, and reproducibility materials. Publicly available supporting materials Extracted Tracker dataset: 10.5281/zenodo.16236175 60 FPS source video: 10.5281/zenodo.17281410 Python peak-detection and histogram scripts: 10.5281/zenodo.17472105 This version should be read as an observational and reproducibility-focused preprint. It is intended to document the measured carrier-period behavior under the stated experimental conditions and to support independent inspection and replication. This paper is designed to be used alongside the public Python script AMC_Carrier_Period_PeakAnalysis_CS3.py, and the corresponding Case Study 3 Dataset dataset hosted on Zenodo. Understanding the histogram: Lower interval values are retained in the plotted distribution for transparency of the extracted peak structure, but the y are not treated in this manuscript as part of the dominant carrier-period estimate. In the accompanying script, peak selection is stabilized using prominence-based detection and minimum-distance thresholding to reduce sensitivity to minor local fluctuations. The reported carrier period is based on the dominant clustered interval band identified under those conditions. Small variations within that band are documented in the manuscript as structured observational features within the detectable envelope; their formal characterization is beyond the scope of this version. Related Works:Measured Carrier-Period Invariance Within the Detectable Envelope of a Coupled Repelling Magnetic Pendulum System: 10.5281/zenodo.20100886Measured 2.5-Cycle Energy Handover in a Coupled Repelling Magnetic Pendulum System: 10.5281/zenodo.20370420Nonlinear Equations of Motion and Multipole Expansion for Active Magnetic Oscillation: 10.5281/zenodo.20649129AMC Dataset — Unified Magnetic Field and Kinetic Energy Dataset - PHASE 2 - (Identical AMC model used in Case Study 3): 10.5281/zenodo.17741166Active Magnetic Cradle — Case Study 3 Source Video Used to Generate Dataset DOI 10.5281/zenodo.16236175: 10.5281/zenodo.17281409Python peak-detection and histogram scripts for carrier-period extraction (Case Study 3): 10.5281/zenodo.17472105ResearchGate profile / discussion layer: https://www.researchgate.net/publication/405103482_Carrier_Period_as_a_Temporal_Signature_in_Coupled_Repelling_Magnetic_Pendula_An_Entry_Point_to_Active_Magnetic_Oscillation_AMO