sketch_cusum.nx

sketch_cusum.nx -- CUSUM change-point detector (Page 1954). Detects shifts in stream mean from a known reference value. Maintains two cumulative sums: S+_t = max(0, S+_{t-1} + (x_t - k - delta)) S-_t = max(0, S-_{t-1} - (x_t - k - delta)) where: k = reference target value (expected mean) delta = slack tolerance (don't alarm on tiny perturbations) ALARM: S+ > h -> upward shift detected (mean increased) S- > h -> downward shift detected (mean decreased) h is the alarm threshold (caller-tuned for false-positive rate). CAPABILITY: - Real-time change-point detection in O(1) state - SRE: latency / error-rate shift detection - manufacturing QC: process drift - finance: regime change - sensor: equipment fault THEORETICAL: Average run length (ARL) under null: ~ exp(h) ARL under shift of size delta: ~ h / delta All integer arithmetic, EXACT semantics. Production tier. LOSSLESS-LANGUAGE DISCIPLINE: alarm verdict is exact (sealed enum-like). nx_cusum_query returns the current statistic with NX_ENV_ABS, param_a = 0.