{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:VEYJVMT74LCQ2KNYPMOZNKIEM2","short_pith_number":"pith:VEYJVMT7","schema_version":"1.0","canonical_sha256":"a9309ab27fe2c50d29b87b1d96a904669cbe33d148c95de9467e0a67a88b0abe","source":{"kind":"arxiv","id":"1407.4835","version":2},"attestation_state":"computed","paper":{"title":"Partial Quantifier Elimination","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Eugene Goldberg, Panagiotis Manolios","submitted_at":"2014-07-17T20:51:37Z","abstract_excerpt":"We consider the problem of Partial Quantifier Elimination (PQE). Given formula exists(X)[F(X,Y) & G(X,Y)], where F, G are in conjunctive normal form, the PQE problem is to find a formula F*(Y) such that F* & exists(X)[G] is logically equivalent to exists(X)[F & G]. We solve the PQE problem by generating and adding to F clauses over the free variables that make the clauses of F with quantified variables redundant. The traditional Quantifier Elimination problem (QE) is a special case of PQE where G is empty so all clauses of the input formula with quantified variables need to be made redundant. "},"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":"1407.4835","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-07-17T20:51:37Z","cross_cats_sorted":[],"title_canon_sha256":"d0660f94598855a6e86584e113adacf9f8c46c63757159c25cda23e157b8ad31","abstract_canon_sha256":"4aef67d16be1cc8e3fbce0831671ef5ebc5a260ff35279058a0ac8e8c99cecde"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:29.771220Z","signature_b64":"ZgOYa9lEXlm6Ay14YA/WJDoYtFnzD28+wosqtETd1x4PF7Gi1a1UCFl5esIfkSl9GYOd5tTAa9V9dDIc3XJTAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9309ab27fe2c50d29b87b1d96a904669cbe33d148c95de9467e0a67a88b0abe","last_reissued_at":"2026-05-18T00:47:29.770775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:29.770775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Partial Quantifier Elimination","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Eugene Goldberg, Panagiotis Manolios","submitted_at":"2014-07-17T20:51:37Z","abstract_excerpt":"We consider the problem of Partial Quantifier Elimination (PQE). Given formula exists(X)[F(X,Y) & G(X,Y)], where F, G are in conjunctive normal form, the PQE problem is to find a formula F*(Y) such that F* & exists(X)[G] is logically equivalent to exists(X)[F & G]. We solve the PQE problem by generating and adding to F clauses over the free variables that make the clauses of F with quantified variables redundant. The traditional Quantifier Elimination problem (QE) is a special case of PQE where G is empty so all clauses of the input formula with quantified variables need to be made redundant. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4835","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":"1407.4835","created_at":"2026-05-18T00:47:29.770852+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.4835v2","created_at":"2026-05-18T00:47:29.770852+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4835","created_at":"2026-05-18T00:47:29.770852+00:00"},{"alias_kind":"pith_short_12","alias_value":"VEYJVMT74LCQ","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"VEYJVMT74LCQ2KNY","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"VEYJVMT7","created_at":"2026-05-18T12:28:52.271510+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/VEYJVMT74LCQ2KNYPMOZNKIEM2","json":"https://pith.science/pith/VEYJVMT74LCQ2KNYPMOZNKIEM2.json","graph_json":"https://pith.science/api/pith-number/VEYJVMT74LCQ2KNYPMOZNKIEM2/graph.json","events_json":"https://pith.science/api/pith-number/VEYJVMT74LCQ2KNYPMOZNKIEM2/events.json","paper":"https://pith.science/paper/VEYJVMT7"},"agent_actions":{"view_html":"https://pith.science/pith/VEYJVMT74LCQ2KNYPMOZNKIEM2","download_json":"https://pith.science/pith/VEYJVMT74LCQ2KNYPMOZNKIEM2.json","view_paper":"https://pith.science/paper/VEYJVMT7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.4835&json=true","fetch_graph":"https://pith.science/api/pith-number/VEYJVMT74LCQ2KNYPMOZNKIEM2/graph.json","fetch_events":"https://pith.science/api/pith-number/VEYJVMT74LCQ2KNYPMOZNKIEM2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VEYJVMT74LCQ2KNYPMOZNKIEM2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VEYJVMT74LCQ2KNYPMOZNKIEM2/action/storage_attestation","attest_author":"https://pith.science/pith/VEYJVMT74LCQ2KNYPMOZNKIEM2/action/author_attestation","sign_citation":"https://pith.science/pith/VEYJVMT74LCQ2KNYPMOZNKIEM2/action/citation_signature","submit_replication":"https://pith.science/pith/VEYJVMT74LCQ2KNYPMOZNKIEM2/action/replication_record"}},"created_at":"2026-05-18T00:47:29.770852+00:00","updated_at":"2026-05-18T00:47:29.770852+00:00"}