sketch_markov.nx

sketch_markov.nx -- discrete-state Markov chain transition tracker. Streaming primitive for sequence modeling. Maintains transition counts t[i][j] = number of times we saw state i followed by state j. At query time, transition probabilities P[i][j] = t[i][j] / Σ_k t[i][k] in PPM (parts per million). USE CASES: - log-event sequence modeling (predict next event class) - DNA / protein sequence analysis - user-behavior modeling (page A -> page B transitions) - failure-mode chains (state transitions toward outage) - text generation (character / word n-grams via k-step extension) CAPABILITY: - online learning: every observation updates state - O(1) per observation - O(N²) memory (N states); caller-bounded - exact integer counts; probabilities in PPM at query time MOST-LIKELY-NEXT-STATE prediction: nx_markov_predict(s) returns the j with max t[s][j]. When ties exist, smallest j wins (deterministic). LOSSLESS-LANGUAGE DISCIPLINE: probabilities in PPM with NX_ENV_ABS param_a = 1 (PPM quantization). Production tier.