Anticipation Geometry

[](LICENSE) [](https://www.rust-lang.org/) [](https://www.python.org/) A mathematical framework that characterizes trajectories through arbitrary state spaces using seven geometric scalars. Originally developed for real-time motion capture at 50 Hz, the framework generalizes to conversational reasoning, knowledge graph traversal, and any sequence of vectors in a metric space. Transition pressure, defined as `d(commitment)/dt - d(uncertainty)/dt`, predicts conversation convergence at **71.8% accuracy** (z = 2.72, p < 0.007). KG-path rewards achieve **100% pairwise ranking accuracy** (Cohen's d = 11.17) on seeded synthetic path evaluation (seed=42), a structural guarantee from chain continuity construction. No domain-specific training is required. | Scalar | Range | What it measures | |--------|-------|-----------------| | **commitment** | [0, 1] | How irreversible the current trajectory state is. High when motion is deep into a sustained phase. | | **uncertainty** | [0, 1] | How many plausible futures remain. High when many historical states are equidistant (gestural regime). | | **transition_pressure** | unbounded | Rate at which futures are collapsing: `d(commitment)/dt - d(uncertainty)/dt`. Positive spikes predict regime changes. | | **recovery_margin** | [0, 1] | Distance to balance/attractor loss. How easy it is to reverse course. | | **phase_stiffness** | [0, 1] | How locked to internal metronome. High directional persistence + low jerk. | | **novelty** | [0, 1] | Distance from recent regime embeddings. High when exploring new territory. | | **stability** | [0, 1] | Local stationarity of dynamics. High predictability + low acceleration. | ### Conversation Convergence (MiniLM, 384D) - **5,000 dialogue turns** across 39 conversations - Transition pressure sign predicts convergence: **71.8% accuracy** - Statistical significance: z = 2.72, p < 0.007 - Transition pressure / commitment correlation: r = 0.455