{"paper":{"title":"Finite Certificates for In-Context Determinacy and a Threshold Theory of Emergence in Language Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.LG","authors_text":"Faruk Alpay, Hamdi Alakkad","submitted_at":"2026-05-30T14:07:58Z","abstract_excerpt":"This paper develops a model-theoretic framework for verifying context-conditioned language-model behavior by replacing benchmark labels with finite semantic certificates. The first problem is finite determinacy: when do examples in a context force the answer to a query without changing model parameters? In finite-field linear task families, we prove an exact row-space criterion, compute the residual hypothesis count, derive full and query-local identification curves, and show that extracting a smallest forcing subcontext is NP-complete even for binary outputs. The second problem is threshold e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07623","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/2606.07623/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"}