Beyond -- Anticipation Geometry for NUMU FARE

Beyond is a NUMU FARE package (`numu-beyond`) that uses anticipation geometry to orchestrate three AI paradigms through a single geometric coordination signal. Instead of each paradigm implementing its own convergence detection, retry logic, and stall recovery, Beyond provides a universal orchestration loop driven by four mathematical scalars computed over the trajectory of bus events. The three paradigms: - **OmniFlow**: Ensemble simulation with counterfactual probing - **Draft-and-Prune**: LLM generation with deterministic verification - **Prompt Optimization**: Search over prompt configurations for quality convergence The key insight: all three follow the same geometric trajectory. They start with high uncertainty and low commitment (exploring), build transition pressure as they narrow (converging), and end with high commitment and low uncertainty (locked). The anticipation scalars make this universal trajectory visible and actionable. These are computed from the trajectory of embedded bus events for each running process. | Scalar | Formula | Range | What it means for orchestration | |--------|---------|-------|---------------------------------| | **commitment** | `1 - \|\|s_t - s_{t-1}\|\| / max_delta` | [0, 1] | How settled the process is. High = outputs are stable. Low = still jumping between approaches. | | **uncertainty** | `H(angles to K nearest neighbors) / H_max` | [0, 1] | How many directions the process could still go. High = many options open. Low = narrowed to one path. | | **transition_pressure** | `d(commitment)/dt - d(uncertainty)/dt` | unbounded | Rate of convergence. Positive spike = decision point approaching. Negative = diverging. | | **recovery_margin** | `1 - min_dist_to_branching_point / max_range` | [0, 1] | Can we backtrack? High = near a decision fork, easy to pivot. Low = deep into a branch, committed. |