{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VEYJVMT74LCQ2KNYPMOZNKIEM2","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":"4aef67d16be1cc8e3fbce0831671ef5ebc5a260ff35279058a0ac8e8c99cecde","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-07-17T20:51:37Z","title_canon_sha256":"d0660f94598855a6e86584e113adacf9f8c46c63757159c25cda23e157b8ad31"},"schema_version":"1.0","source":{"id":"1407.4835","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4835","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4835v2","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4835","created_at":"2026-05-18T00:47:29Z"},{"alias_kind":"pith_short_12","alias_value":"VEYJVMT74LCQ","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"VEYJVMT74LCQ2KNY","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"VEYJVMT7","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:885c00f6f6c3d98113bd868024214d4d416fffcb89bee4c183665c94c1d7d9e5","target":"graph","created_at":"2026-05-18T00:47:29Z","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":"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. ","authors_text":"Eugene Goldberg, Panagiotis Manolios","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-07-17T20:51:37Z","title":"Partial Quantifier Elimination"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4835","kind":"arxiv","version":2},"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:d721cbe2e90ab79da2126e00c088e98ba83e498f33cfac8d53b198a13944bf9f","target":"record","created_at":"2026-05-18T00:47:29Z","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":"4aef67d16be1cc8e3fbce0831671ef5ebc5a260ff35279058a0ac8e8c99cecde","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-07-17T20:51:37Z","title_canon_sha256":"d0660f94598855a6e86584e113adacf9f8c46c63757159c25cda23e157b8ad31"},"schema_version":"1.0","source":{"id":"1407.4835","kind":"arxiv","version":2}},"canonical_sha256":"a9309ab27fe2c50d29b87b1d96a904669cbe33d148c95de9467e0a67a88b0abe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9309ab27fe2c50d29b87b1d96a904669cbe33d148c95de9467e0a67a88b0abe","first_computed_at":"2026-05-18T00:47:29.770775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:29.770775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZgOYa9lEXlm6Ay14YA/WJDoYtFnzD28+wosqtETd1x4PF7Gi1a1UCFl5esIfkSl9GYOd5tTAa9V9dDIc3XJTAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:29.771220Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4835","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d721cbe2e90ab79da2126e00c088e98ba83e498f33cfac8d53b198a13944bf9f","sha256:885c00f6f6c3d98113bd868024214d4d416fffcb89bee4c183665c94c1d7d9e5"],"state_sha256":"f185eb460e6528bdd71c8748e22e6851e43dd0e40af04c9d8816d17543b67e76"}