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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","authors_text":"Leonid Dorochko, Micha{\\l} Wrona","cross_cats":["cs.LO"],"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.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-01-30T08:11:38Z","title":"Constraint Satisfaction Problems over Finitely Bounded Homogeneous Structures: a Dichotomy between FO and L-hard"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.22691","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-16T09:57:13.236447Z","id":"06e9228e-349f-4cf1-adf1-ce9f17e7f29b","model_set":{"reader":"grok-4.3"},"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","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.","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.","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."}},"verdict_id":"06e9228e-349f-4cf1-adf1-ce9f17e7f29b"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:613403808c093d3d6e6893787a90ea14da07d08fdd0aa21618c7895a935b1f57","target":"record","created_at":"2026-07-16T00:21:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ca85770be484f9c02dbd1562c5e78dcea9f6340ece59a088f8f46207698ade2c","cross_cats_sorted":["cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-01-30T08:11:38Z","title_canon_sha256":"a7223a041d78f2a8545026edc9c7cf9469dca91531babdd77c18388d0d857691"},"schema_version":"1.0","source":{"id":"2601.22691","kind":"arxiv","version":3}},"canonical_sha256":"729d7f04d950e2e0da153a443174ae294f01f826dcaab1b76ac2a6ee5f2f8e8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"729d7f04d950e2e0da153a443174ae294f01f826dcaab1b76ac2a6ee5f2f8e8f","first_computed_at":"2026-07-16T00:21:44.897051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-16T00:21:44.897051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dg4nJE3SGOvN95wvK7WpdZU17G6Zh6FHOSUO0qMhkfehwAA7gq9qSDv3djzYHoGpB+McWjg2Xco0AWNVkAb5DA==","signature_status":"signed_v1","signed_at":"2026-07-16T00:21:44.897983Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.22691","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:613403808c093d3d6e6893787a90ea14da07d08fdd0aa21618c7895a935b1f57","sha256:08ce1c0040fb084290bd86e241e57b44e45590af53d6bc6ad8dc055380f54c8a"],"state_sha256":"5be3f63b21936ff1be07980cc5a37b7898d1b654d8053c1cc007da337a67a2eb"}