{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:HQ3A26LIWDGQNWP5XJFXMYZITO","short_pith_number":"pith:HQ3A26LI","schema_version":"1.0","canonical_sha256":"3c360d7968b0cd06d9fdba4b7663289bab6d13988a89d83046bc5d68daebe505","source":{"kind":"arxiv","id":"1108.5288","version":4},"attestation_state":"computed","paper":{"title":"The expressibility of functions on the Boolean domain, with applications to Counting CSPs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Andrei A. Bulatov, Colin McQuillan, Leslie Ann Goldberg, Mark Jerrum, Martin Dyer","submitted_at":"2011-08-26T12:54:13Z","abstract_excerpt":"An important tool in the study of the complexity of Constraint Satisfaction Problems (CSPs) is the notion of a relational clone, which is the set of all relations expressible using primitive positive formulas over a particular set of base relations. Post's lattice gives a complete classification of all Boolean relational clones, and this has been used to classify the computational difficulty of CSPs. Motivated by a desire to understand the computational complexity of (weighted) counting CSPs, we develop an analogous notion of functional clones and study the landscape of these clones. One of th"},"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":"1108.5288","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-08-26T12:54:13Z","cross_cats_sorted":[],"title_canon_sha256":"b9c799b42cb305385f7da817ccc4f0af4f917f6b417815cbbc93483abf7c0d94","abstract_canon_sha256":"a2b5841301a6185df4d9c69ac1d8cf4530532451ce697130d52e157150da6409"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:20.407021Z","signature_b64":"Fr8ZvFq/qOlo50TS72KgXgxTsYTlpRv8wvHWSso20G61LS6vAZebysPF3KuushY7w3Vr2S4nrNMK0hsa0T/QBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c360d7968b0cd06d9fdba4b7663289bab6d13988a89d83046bc5d68daebe505","last_reissued_at":"2026-05-18T03:09:20.406237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:20.406237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The expressibility of functions on the Boolean domain, with applications to Counting CSPs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Andrei A. Bulatov, Colin McQuillan, Leslie Ann Goldberg, Mark Jerrum, Martin Dyer","submitted_at":"2011-08-26T12:54:13Z","abstract_excerpt":"An important tool in the study of the complexity of Constraint Satisfaction Problems (CSPs) is the notion of a relational clone, which is the set of all relations expressible using primitive positive formulas over a particular set of base relations. Post's lattice gives a complete classification of all Boolean relational clones, and this has been used to classify the computational difficulty of CSPs. Motivated by a desire to understand the computational complexity of (weighted) counting CSPs, we develop an analogous notion of functional clones and study the landscape of these clones. One of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5288","kind":"arxiv","version":4},"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":"1108.5288","created_at":"2026-05-18T03:09:20.406382+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.5288v4","created_at":"2026-05-18T03:09:20.406382+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5288","created_at":"2026-05-18T03:09:20.406382+00:00"},{"alias_kind":"pith_short_12","alias_value":"HQ3A26LIWDGQ","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"HQ3A26LIWDGQNWP5","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"HQ3A26LI","created_at":"2026-05-18T12:26:30.835961+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/HQ3A26LIWDGQNWP5XJFXMYZITO","json":"https://pith.science/pith/HQ3A26LIWDGQNWP5XJFXMYZITO.json","graph_json":"https://pith.science/api/pith-number/HQ3A26LIWDGQNWP5XJFXMYZITO/graph.json","events_json":"https://pith.science/api/pith-number/HQ3A26LIWDGQNWP5XJFXMYZITO/events.json","paper":"https://pith.science/paper/HQ3A26LI"},"agent_actions":{"view_html":"https://pith.science/pith/HQ3A26LIWDGQNWP5XJFXMYZITO","download_json":"https://pith.science/pith/HQ3A26LIWDGQNWP5XJFXMYZITO.json","view_paper":"https://pith.science/paper/HQ3A26LI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.5288&json=true","fetch_graph":"https://pith.science/api/pith-number/HQ3A26LIWDGQNWP5XJFXMYZITO/graph.json","fetch_events":"https://pith.science/api/pith-number/HQ3A26LIWDGQNWP5XJFXMYZITO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HQ3A26LIWDGQNWP5XJFXMYZITO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HQ3A26LIWDGQNWP5XJFXMYZITO/action/storage_attestation","attest_author":"https://pith.science/pith/HQ3A26LIWDGQNWP5XJFXMYZITO/action/author_attestation","sign_citation":"https://pith.science/pith/HQ3A26LIWDGQNWP5XJFXMYZITO/action/citation_signature","submit_replication":"https://pith.science/pith/HQ3A26LIWDGQNWP5XJFXMYZITO/action/replication_record"}},"created_at":"2026-05-18T03:09:20.406382+00:00","updated_at":"2026-05-18T03:09:20.406382+00:00"}