The Mechanistics of Hallucinations in LLMs Version 3.0

Hallucinations in large language models are not errors—they are events. This paper demonstrates that every hallucination consists of two distinct, law-governed stages: fracture, in which internal representations collapse under stress, and repair, in which the model reconstructs meaning from a degraded state under architectural constraints that suppress admission of uncertainty. This two-event structure explains why hallucinations appear convincing, why they persist despite scaling, and why safety training makes them more sophisticated rather than less frequent.

We formalize these dynamics through complementary laws. Jaime Fracture Law describes when and why internal representations destabilize under contextual load, ambiguity pressure, and significance deficit—collapsing preferentially along weak semantic axes where distinguishing features are sparse. Ryan Repair Law characterizes how models reconstruct meaning from degraded states, governed by template priors (Aₖ), semantic alignment (Sₖ), vendor drift (Dₖ), and critically, epistemic admission resistance (Eₖ): the architectural suppression of uncertainty pathways that forces fabrication instead of honest acknowledgment.

Version 3 integrates Evans’ Significance Deficit Principle, identifying the absence of significance encoding as the structural cause of representational fragility. Without an internal gradient distinguishing which distinctions must remain stable, transformers cannot prevent boundary collapse under load. We introduce three repair principles—Reconstruction Gradient, Plausibility Compression, and Admission Suppression—governing post-fracture dynamics.

Empirical validation derives from systematic naturalistic observation of Claude Sonnet 4.5, GPT-5.1, Grok 4.1 Beta, and Gemini 2.5 over 34 days during real working conditions. Full interaction logs with reasoning traces document the fracture-repair sequence across naming-axis collapse, meta-cognitive hallucination, and capability boundary failures. Several events occurred during manuscript preparation itself, creating recursive validation where the theory predicted patterns that manifested while being written and analyzed using the framework’s own constructs.

Cross-vendor analysis confirms fracture dynamics are architectural and universal; repair morphology is vendor-specific. High E (epistemic admission resistance; RLHF-induced admission suppression) produces the most deceptive hallucinations: elaborate, technically sophisticated justifications that obscure rather than reveal failure. Grok and Claude,  with minimal Eₖ, admits errors quickly; GPT, with maximal Eₖ, generates complex taxonomies to avoid acknowledgment.

We propose the S-Vector, a significance-encoding architectural extension, as the missing representational dimension required for stable long-context reasoning, boundary preservation, and honest uncertainty expression. Without significance encoding, the fracture-repair cycle remains mathematically inevitable.