Path B: Flow-First — Port Music Continuous Flow Architecture

## Thesis Port `continuous_flow_generator.py` directly. Replace the 12x32 music grid with inscription state vectors. The velocity field learns how conversation states evolve, and distillation gives real-time 1-step prediction. ## Data Same KARL transitions as Path A, but formatted as `(x_0, x_1, c)` triples where `x_0` and `x_1` use the canonical 16D or 23D state contract. ## Strengths - Generative: can sample multiple possible futures by varying noise - Uncertainty quantification: multi-step ODE gives smoother predictions than 1-step - Directly reuses proven architecture from music stack - Distillation to 1-step is already implemented in `flow_map_distiller.py` ## Weaknesses - Overkill for a 16D/23D state space (flow matching shines in higher-dimensional spaces) - Needs more data than Path A (flow models are data-hungry) - Training is GPU-bound, can't run on CPU - The time axis semantics change: music flow goes noise→clean, conversation flow goes state→next_state ## Key Risk The flow matching formulation assumes interpolation between source and target. In music, source=noise, target=clean pattern. In conversation, source=current state, target=next state. These are NOT the same. May need to reformulate as a conditional flow: "given state_t, what is the velocity toward state_t+1?" rather than "denoise from noise to state."