Direction, Not Depth: A Directional Criterion for Distinguishing Productive from Pathological Attractors in Latent Reasoning

Latent and recurrent reasoning in language models tends to converge to fixed points, and a growing body of work distinguishes good from bad trajectories by outcome signatures: correct reasoning converges while incorrect reasoning scatters; factual generation follows a path toward a stable attractor while hallucination drifts. These signatures are read at or near the endpoint, and they answer the question did this trajectory succeed? after the fact. They do not answer two prior questions: which fixed point is worth converging to, and how can we tell, in process, before the outcome? This paper argues that the discriminating quantity for both is directional, not magnitudinal. A "strong" or deep attractor is not therefore a legitimate one — the strongest basin a refinement process can fall into is often degenerate (repetition, mode collapse, self-referential fixation). I propose distinguishing a releasing trajectory — one whose displacement keeps advancing toward a target and passes through rather than returning to its origin — from a trapping trajectory — one that curls back into a self-referential basin regardless of that basin's depth. The criterion is available in process and orthogonal to strength. A control corollary follows: escaping a trapping basin is better served by minimal, angle-correcting steering than by high-magnitude forcing. I give falsifiable predictions and the conditions under which the whole proposal fails.