{"paper":{"title":"Constraint Satisfaction Problems over Finitely Bounded Homogeneous Structures: a Dichotomy between FO and L-hard","license":"http://creativecommons.org/licenses/by/4.0/","headline":"CSPs over first-order expansions of finitely bounded homogeneous model-complete cores are either first-order definable or L-hard under first-order reduction.","cross_cats":["cs.LO"],"primary_cat":"cs.CC","authors_text":"Leonid Dorochko, Micha{\\l} Wrona","submitted_at":"2026-01-30T08:11:38Z","abstract_excerpt":"Feder-Vardi conjecture, which proposed that every finite-domain Constraint Satisfaction Problem (CSP) is either in P or it is NP-complete, has been solved independently by Bulatov and Zhuk almost ten years ago. Bodirsky-Pinsker conjecture which states a similar dichotomy for countably infinite first-order reducts of finitely bounded homogeneous structures is wide open.\n  In this paper, we prove that CSPs over first-order expansions of finitely bounded homogeneous model-complete cores are either first-order definable (and hence in non-uniform AC$^0$) or L-hard under first-order reduction. It is"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"CSPs over first-order expansions of finitely bounded homogeneous model-complete cores are either first-order definable (and hence in non-uniform AC0) or L-hard under first-order reduction.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The structures under consideration are model-complete cores and the new proof of the Larose-Tesson theorem for finite structures lifts directly to the infinite case without additional hidden assumptions on the reducts.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"CSPs over FO expansions of finitely bounded homogeneous model-complete cores are either FO-definable (in non-uniform AC0) or L-hard under FO reductions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"CSPs over first-order expansions of finitely bounded homogeneous model-complete cores are either first-order definable or L-hard under first-order reduction.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a3af9dbfbf72c8a9fece194a035cd520c9e34fc107ee06e06ef3b3614728d68c"},"source":{"id":"2601.22691","kind":"arxiv","version":3},"verdict":{"id":"06e9228e-349f-4cf1-adf1-ce9f17e7f29b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T09:57:13.236447Z","strongest_claim":"CSPs over first-order expansions of finitely bounded homogeneous model-complete cores are either first-order definable (and hence in non-uniform AC0) or L-hard under first-order reduction.","one_line_summary":"CSPs over FO expansions of finitely bounded homogeneous model-complete cores are either FO-definable (in non-uniform AC0) or L-hard under FO reductions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The structures under consideration are model-complete cores and the new proof of the Larose-Tesson theorem for finite structures lifts directly to the infinite case without additional hidden assumptions on the reducts.","pith_extraction_headline":"CSPs over first-order expansions of finitely bounded homogeneous model-complete cores are either first-order definable or L-hard under first-order reduction."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.22691/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"}