Prime-power indexed multiscale graph diagnostics for symbolic temporal data: methodological exploration and delimitation via BWV 1007

This short methodological note examines the prime-power indexed multiscale graph diagnostic on a single, thoroughly annotated test case: the six movements of J. S. Bach's Cello Suite No. 1 in G major (BWV 1007). Using four MIDI editions and both beat-synchronised and seconds-based time axes, we map the sensitivity of the beta₀ separation diagnostic to edition choice, time-axis discretisation, and kNN neighbourhood size. The analysis delimits the regime in which the diagnostic is informative and identifies the conditions under which it degenerates. This note serves as a companion to the full profinite/p-adic framework paper. Companion reproducibility bundle: https: //doi. org/10. 5281/zenodo. 19837174Companion framework paper: https: //doi. org/10. 5281/zenodo. 19837367