PRINCIPAL CURVE NOVELTY GEOMETRY: FALSIFIABLE ATTRIBUTION OF NOVELTY IN FROZEN SEQUENTIAL REPRESENTATIONS

Post-hoc novelty methods usually reduce representation unusualness to a single scalar, obscuring whether an observation is unusual because of its position along a learned trajectory, its deviation from that trajectory, or its rate of progression. We introduce principal-curve novelty geometry (PCNG), a post-hoc measurement con- tract for frozen sequential representations that asks which geometric interpretation is supported and when attribution should be refused. PCNG fits a training-only principal curve, tests whether the resulting progression geometry is admissible, and, when permitted, derives progression, transverse deviation and traversal rate on a common rarity scale calibrated against the training reference. Targeted interventions test these interpretations, while unit-preserving randomisation evalu- ates residual coupling beyond the dependence already present within trajectories. Across 117 runs in degradation prognostics spanning 13 frozen configurations, failure-mode interventions support the transverse interpretation in 35 of 36 di- rected tests, whereas the rate interpretation is unsupported. Cross-unit scrambling reduces the transverse hit rate from 0.972 to 0.667, while a within-unit control remains at 1.000. Residual coupling is heterogeneous, precluding an independence claim; the admissibility gate also varies across encoders and rejects some external- domain runs. Operationally, transverse rarity yields a 4.9% false-alarm rate versus 29.2% for a learned early-degradation health monitor at matched coverage, while distance-based novelty remains competitive. PCNG therefore contributes falsifiable attribution rather than universally better detection.