{"paper":{"title":"The Anatomy of a Truth Direction: Knowledge-Dependent Dimensionality, a Relational Law, and a Convergent Category Geometry in Small Language Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Francesco Karim Vicidomini","submitted_at":"2026-07-18T10:03:21Z","abstract_excerpt":"B\\\"urger et al. (2024) demonstrated that truth representations in large language models are universal across statement polarity but reside within a multidimensional subspace. We extend that framework along three questions: how the dimensionality of the subspace depends on the model's knowledge, which architectural component builds the truth direction, and what the direction is a mixture of. In Part I (one model), a training-free directional probe derived from the SVD of hidden-state minimal pairs shows that the dimensionality of truth is knowledge-dependent: the signal is concentrated on a sin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16741","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.16741/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}