{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:N5SNKTZYGGDULXJ5LU62FQAU24","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"48efd90bc8a5fda6c89f5e4dc633a6c7e26e0754f7784f850dcea51eabfa42c9","cross_cats_sorted":["cs.DB","cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-08-05T08:46:17Z","title_canon_sha256":"e3924b528f09bfa2bcd024f84fb3b87058092a8f4777ed61b425b3755daec05b"},"schema_version":"1.0","source":{"id":"1408.0890","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.0890","created_at":"2026-05-18T02:29:01Z"},{"alias_kind":"arxiv_version","alias_value":"1408.0890v3","created_at":"2026-05-18T02:29:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0890","created_at":"2026-05-18T02:29:01Z"},{"alias_kind":"pith_short_12","alias_value":"N5SNKTZYGGDU","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N5SNKTZYGGDULXJ5","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N5SNKTZY","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:03914737b38e7f0c0eadaf0208abafd2448033d1979c9e2fbfa9f8a5cd5d5f69","target":"graph","created_at":"2026-05-18T02:29:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Conjunctive queries are basic and heavily studied database queries; in relational algebra, they are the select-project-join queries. In this article, we study the fundamental problem of counting, given a conjunctive query and a relational database, the number of answers to the query on the database. In particular, we study the complexity of this problem relative to sets of conjunctive queries. We present a trichotomy theorem, which shows essentially that this problem on a set of conjunctive queries is either tractable, equivalent to the parameterized CLIQUE problem, or as hard as the parameter","authors_text":"Hubie Chen, Stefan Mengel","cross_cats":["cs.DB","cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-08-05T08:46:17Z","title":"A Trichotomy in the Complexity of Counting Answers to Conjunctive Queries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0890","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f856b470402fc287a9a677ea9c69ddabd7404af68481a13a49b0c938695ae11a","target":"record","created_at":"2026-05-18T02:29:01Z","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":"48efd90bc8a5fda6c89f5e4dc633a6c7e26e0754f7784f850dcea51eabfa42c9","cross_cats_sorted":["cs.DB","cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-08-05T08:46:17Z","title_canon_sha256":"e3924b528f09bfa2bcd024f84fb3b87058092a8f4777ed61b425b3755daec05b"},"schema_version":"1.0","source":{"id":"1408.0890","kind":"arxiv","version":3}},"canonical_sha256":"6f64d54f38318745dd3d5d3da2c014d738514745e0a457e2b63806bc4a11b7aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f64d54f38318745dd3d5d3da2c014d738514745e0a457e2b63806bc4a11b7aa","first_computed_at":"2026-05-18T02:29:01.399886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:01.399886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bn2tAZmS4mNsFiNgxBNsL3gjDXnkCWe1A7POx7fPU2x4xHdCCoCRedMspqLe7PLXHAEe9al//ix6FU4RKfcPAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:01.400346Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.0890","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f856b470402fc287a9a677ea9c69ddabd7404af68481a13a49b0c938695ae11a","sha256:03914737b38e7f0c0eadaf0208abafd2448033d1979c9e2fbfa9f8a5cd5d5f69"],"state_sha256":"01ce51f04c4f4ca3836b868da2f1c1dc2316194da5b945e4802ffca7d1f03e3b"}