Abstract: In music beat tracking, model-predicted activations must be decoded into a discrete, musically coherent event sequence. Direct peak picking closely follows local evidence but can retain spurious peaks or miss weak beats. Dynamic Bayesian networks (DBNs), a widely used structured post-processor, improve sequence consistency under predefined global tempo, meter, and transition constraints, but their behavior can depend strongly on these settings. We introduce CASM, a context-aware semi-Markov decoder that instead conditions its temporal constraint on local activation evidence. CASM also accounts for ambiguity among competing periodic interpretations, including half- and double-tempo alternatives. Deterministic safeguards prevent implausible outputs and preserve beat-downbeat consistency. Applied to fixed activations from three neural beat trackers (BeatThis, MSCNN, and TCN), CASM improves temporal continuity while preserving event-level F1 across the GTZAN and SMC datasets, without backbone retraining or dataset-specific retuning. Further analysis shows that CASM is less sensitive than the DBN baseline to the composition of the calibration data.