Hallucination as Signal and Structural Prediction: A Cascade of Hypotheses on Latent Space Geometry, Cross-Model Knowledge Routing, and Prediction Beyond the Knowledge Horizon

This paper presents a cascade of three linked hypotheses on the nature of LLM hallucination, each building on the previous with decreasing confidence and increasing scope. Hypothesis I (high confidence): hallucination is a structured directional signal in latent space — a vector produced by extrapolation beyond the model's trained knowledge manifold, not a stochastic failure. A parent-child model experiment is proposed: the small model's boundary vector is projected into the parent's latent space via a gamut mapping function; the parent resumes inference from that address. Cache miss becomes a pointer, not a failure. Hypothesis II (medium confidence): applying the same logic one level up — the boundary vectors of a large model point toward knowledge beyond the current horizon of human-recorded knowledge. Structurally grounded predictions, not random errors. Retrospectively falsifiable. Hypothesis III (speculative): systematic extraction of these boundary vectors constitutes a mechanism for directed scientific hypothesis generation — geometry-constrained extrapolation replacing undirected search. Each hypothesis carries an explicit confidence level and falsification condition. Integration with the R-State framework is described: a model at its knowledge boundary emits a latent vector as an R-State packet rather than a confabulated token sequence, transforming hallucination into a routing event.