{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:QXGX6KV562DZGID2IFGY5ZWGDC","short_pith_number":"pith:QXGX6KV5","schema_version":"1.0","canonical_sha256":"85cd7f2abdf68793207a414d8ee6c6189ae2792b151595a114980a134491f463","source":{"kind":"arxiv","id":"1412.1505","version":3},"attestation_state":"computed","paper":{"title":"Symmetric Weighted First-Order Model Counting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CC","cs.LO"],"primary_cat":"cs.DB","authors_text":"Dan Suciu, Eric Gribkoff, Guy Van den Broeck, Paul Beame","submitted_at":"2014-12-03T22:03:52Z","abstract_excerpt":"The FO Model Counting problem (FOMC) is the following: given a sentence $\\Phi$ in FO and a number $n$, compute the number of models of $\\Phi$ over a domain of size $n$; the Weighted variant (WFOMC) generalizes the problem by associating a weight to each tuple and defining the weight of a model to be the product of weights of its tuples. In this paper we study the complexity of the symmetric WFOMC, where all tuples of a given relation have the same weight. Our motivation comes from an important application, inference in Knowledge Bases with soft constraints, like Markov Logic Networks, but the "},"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":"1412.1505","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2014-12-03T22:03:52Z","cross_cats_sorted":["cs.AI","cs.CC","cs.LO"],"title_canon_sha256":"3930b993edbdd30714b2e1dd1fd7aa07d9bcf065d63c047a1b3b7c394919b874","abstract_canon_sha256":"a364712a34dc5b08cf4788e0c1891fdcd06ed93ed092f2b1239f55ca12424e16"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:58.082254Z","signature_b64":"182rktUKEfp2LWwklTRO+NHQiuOyX1/D0gt+RumL8DbK6kv/fqmFhc19k7snDP1llsDf1GkJLt2YGu7UuKrPDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85cd7f2abdf68793207a414d8ee6c6189ae2792b151595a114980a134491f463","last_reissued_at":"2026-05-18T01:59:58.081742Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:58.081742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetric Weighted First-Order Model Counting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CC","cs.LO"],"primary_cat":"cs.DB","authors_text":"Dan Suciu, Eric Gribkoff, Guy Van den Broeck, Paul Beame","submitted_at":"2014-12-03T22:03:52Z","abstract_excerpt":"The FO Model Counting problem (FOMC) is the following: given a sentence $\\Phi$ in FO and a number $n$, compute the number of models of $\\Phi$ over a domain of size $n$; the Weighted variant (WFOMC) generalizes the problem by associating a weight to each tuple and defining the weight of a model to be the product of weights of its tuples. In this paper we study the complexity of the symmetric WFOMC, where all tuples of a given relation have the same weight. Our motivation comes from an important application, inference in Knowledge Bases with soft constraints, like Markov Logic Networks, but the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1505","kind":"arxiv","version":3},"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":"1412.1505","created_at":"2026-05-18T01:59:58.081820+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.1505v3","created_at":"2026-05-18T01:59:58.081820+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1505","created_at":"2026-05-18T01:59:58.081820+00:00"},{"alias_kind":"pith_short_12","alias_value":"QXGX6KV562DZ","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"QXGX6KV562DZGID2","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"QXGX6KV5","created_at":"2026-05-18T12:28:46.137349+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/QXGX6KV562DZGID2IFGY5ZWGDC","json":"https://pith.science/pith/QXGX6KV562DZGID2IFGY5ZWGDC.json","graph_json":"https://pith.science/api/pith-number/QXGX6KV562DZGID2IFGY5ZWGDC/graph.json","events_json":"https://pith.science/api/pith-number/QXGX6KV562DZGID2IFGY5ZWGDC/events.json","paper":"https://pith.science/paper/QXGX6KV5"},"agent_actions":{"view_html":"https://pith.science/pith/QXGX6KV562DZGID2IFGY5ZWGDC","download_json":"https://pith.science/pith/QXGX6KV562DZGID2IFGY5ZWGDC.json","view_paper":"https://pith.science/paper/QXGX6KV5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.1505&json=true","fetch_graph":"https://pith.science/api/pith-number/QXGX6KV562DZGID2IFGY5ZWGDC/graph.json","fetch_events":"https://pith.science/api/pith-number/QXGX6KV562DZGID2IFGY5ZWGDC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QXGX6KV562DZGID2IFGY5ZWGDC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QXGX6KV562DZGID2IFGY5ZWGDC/action/storage_attestation","attest_author":"https://pith.science/pith/QXGX6KV562DZGID2IFGY5ZWGDC/action/author_attestation","sign_citation":"https://pith.science/pith/QXGX6KV562DZGID2IFGY5ZWGDC/action/citation_signature","submit_replication":"https://pith.science/pith/QXGX6KV562DZGID2IFGY5ZWGDC/action/replication_record"}},"created_at":"2026-05-18T01:59:58.081820+00:00","updated_at":"2026-05-18T01:59:58.081820+00:00"}