{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:OMDTTK7GXVFQ56QGONVKGN3OFY","short_pith_number":"pith:OMDTTK7G","schema_version":"1.0","canonical_sha256":"730739abe6bd4b0efa06736aa3376e2e25d8d38f68070e06cb4ab9c71f62d47f","source":{"kind":"arxiv","id":"cs/0612069","version":2},"attestation_state":"computed","paper":{"title":"Cores of Countably Categorical Structures","license":"","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Manuel Bodirsky","submitted_at":"2006-12-13T09:59:56Z","abstract_excerpt":"A relational structure is a core, if all its endomorphisms are embeddings. This notion is important for computational complexity classification of constraint satisfaction problems. It is a fundamental fact that every finite structure has a core, i.e., has an endomorphism such that the structure induced by its image is a core; moreover, the core is unique up to isomorphism. Weprove that every \\omega -categorical structure has a core. Moreover, every \\omega-categorical structure is homomorphically equivalent to a model-complete core, which is unique up to isomorphism, and which is finite or \\ome"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"cs/0612069","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cs.LO","submitted_at":"2006-12-13T09:59:56Z","cross_cats_sorted":[],"title_canon_sha256":"4ff8538b4353c474e761fc5834389a8194f26207fe2ab49a1bd5d95ef0cf298b","abstract_canon_sha256":"509f8d6b859485f6657327de0d9fbec837a3f4bf4a9ea9967695360d5381d58e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:03.263479Z","signature_b64":"JwaOyQ62sKqEJeI92r2JOwfzYEeG7o3sVdJl/HQ5uE+5HF7SEWeDlch7f7PZgJTLFrG7eT2ZPsqUshKSVVq+Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"730739abe6bd4b0efa06736aa3376e2e25d8d38f68070e06cb4ab9c71f62d47f","last_reissued_at":"2026-05-18T00:53:03.263016Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:03.263016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cores of Countably Categorical Structures","license":"","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Manuel Bodirsky","submitted_at":"2006-12-13T09:59:56Z","abstract_excerpt":"A relational structure is a core, if all its endomorphisms are embeddings. This notion is important for computational complexity classification of constraint satisfaction problems. It is a fundamental fact that every finite structure has a core, i.e., has an endomorphism such that the structure induced by its image is a core; moreover, the core is unique up to isomorphism. Weprove that every \\omega -categorical structure has a core. Moreover, every \\omega-categorical structure is homomorphically equivalent to a model-complete core, which is unique up to isomorphism, and which is finite or \\ome"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0612069","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"cs/0612069","created_at":"2026-05-18T00:53:03.263090+00:00"},{"alias_kind":"arxiv_version","alias_value":"cs/0612069v2","created_at":"2026-05-18T00:53:03.263090+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0612069","created_at":"2026-05-18T00:53:03.263090+00:00"},{"alias_kind":"pith_short_12","alias_value":"OMDTTK7GXVFQ","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"OMDTTK7GXVFQ56QG","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"OMDTTK7G","created_at":"2026-05-18T12:25:54.717736+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OMDTTK7GXVFQ56QGONVKGN3OFY","json":"https://pith.science/pith/OMDTTK7GXVFQ56QGONVKGN3OFY.json","graph_json":"https://pith.science/api/pith-number/OMDTTK7GXVFQ56QGONVKGN3OFY/graph.json","events_json":"https://pith.science/api/pith-number/OMDTTK7GXVFQ56QGONVKGN3OFY/events.json","paper":"https://pith.science/paper/OMDTTK7G"},"agent_actions":{"view_html":"https://pith.science/pith/OMDTTK7GXVFQ56QGONVKGN3OFY","download_json":"https://pith.science/pith/OMDTTK7GXVFQ56QGONVKGN3OFY.json","view_paper":"https://pith.science/paper/OMDTTK7G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cs/0612069&json=true","fetch_graph":"https://pith.science/api/pith-number/OMDTTK7GXVFQ56QGONVKGN3OFY/graph.json","fetch_events":"https://pith.science/api/pith-number/OMDTTK7GXVFQ56QGONVKGN3OFY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OMDTTK7GXVFQ56QGONVKGN3OFY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OMDTTK7GXVFQ56QGONVKGN3OFY/action/storage_attestation","attest_author":"https://pith.science/pith/OMDTTK7GXVFQ56QGONVKGN3OFY/action/author_attestation","sign_citation":"https://pith.science/pith/OMDTTK7GXVFQ56QGONVKGN3OFY/action/citation_signature","submit_replication":"https://pith.science/pith/OMDTTK7GXVFQ56QGONVKGN3OFY/action/replication_record"}},"created_at":"2026-05-18T00:53:03.263090+00:00","updated_at":"2026-05-18T00:53:03.263090+00:00"}