Ô Framework × NASA C-MAPSS: Condition-Normalization Confirms Structural Decoupling

The Ô (O-Hat) cusp-catastrophe degradation signal is extracted from all four NASA C-MAPSS turbofan datasets, with operating-condition confound eliminated by linear-residual normalization. Key Findings Single-condition (FD001/003): Ô detects 66–83% of engines with genuine degradation transitions — no normalization needed. Multi-condition raw (FD002/004): 111σ COLLAPSE signatures are entirely artifact — operating-condition switching, not degradation. Multi-condition normalized: Linear-residual normalization (s9 ~ op1+op2+op3) collapses FD002/004 to 91%+ CONTINUOUS_FLOW, with 8–9% genuine transitions and max deviations of 12–13σ. Significance This is Ô's first engineering case study that actively uses normalization to decouple confound from signal. It establishes a general workflow pattern — confound identification → normalization → Ô analysis — applicable to any engineering system with known operating regime confounds. The same approach is directly transferable to LLM attention analysis (seq length as confound) and industrial prognostics (RUL prediction from degradation transition onset). Document 8-section technical report (~1,800 words, 4 tables). Part of the Ô Framework Zenodo family.