CHORD: Resolving 12-h Transcriptomic Rhythms Into Harmonic, Autonomous, and Intersection Origins

A 12-h (12-h) periodicity in a transcriptomic series is routinely reported as a "12-h rhythm," yet a single 12-h spectral peak can arise from 3 mechanistically distinct processes: the second harmonic of a non-sinusoidal 24-h waveform (a harmonic), an autonomous 12-h oscillator with its own phase (such as the IRE1$\alpha$-XBP1s ER-stress cycle), or the apparent 12-h when 2 anti-phase 24-h processes combine as synthesis minus degradation (an intersection). These origins carry opposite biological meanings but are indistinguishable to standard detectors such as JTK_CYCLE, RAIN, and Cosinor. To resolve the origin of 12-h rhythms, Circadian Harmonic Oscillation Resolution and Disentanglement (CHORD) detects 12-h periodicity and resolves it into this ternary taxonomy. Detection fuses 4 tests through the Cauchy Combination Test; disentanglement rests on 4 complementary statistics, each tied to one identifiable model feature and combined by a calibrated multinomial classifier. On a held-out benchmark, CHORD separates autonomous from driven 12 h at area under the curve (AUC) 0.83 and a genuine oscillator from an intersection at 0.93. An interventional test anchors the classifier to biology: in a liver-specific XBP1 knockout, the hepatic 12-h program collapses when the IRE1-XBP1 clock is ablated (knockout/wild-type ratio 0.27) while the 24-h circadian clock is preserved (0.91). The canonical autonomous genes are 12-h dominant with little 24 h, which a single series cannot resolve, so CHORD abstains and the intervention resolves them; the confidently classified autonomous set also collapses more than the driven set (0.47 vs. 0.62). Because the program is strongly coregulated, a correlation-adjusted test keeps the program-versus-driven collapse significant ($p=00.045$); this validation covers the autonomous arm in liver only. An identifiability budget shows that 12-h signal-to-noise, not sampling density, bounds classification. CHORD reframes ultradian transcriptomics from whether a 12-h rhythm exists to what kind it is.