{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:QFSHYRJEXQOXC4K6SGOPEYVHDP","short_pith_number":"pith:QFSHYRJE","schema_version":"1.0","canonical_sha256":"81647c4524bc1d71715e919cf262a71bfe1be8c477457520ed26a4d0a36bbd9b","source":{"kind":"arxiv","id":"1601.04802","version":3},"attestation_state":"computed","paper":{"title":"Interpolation synthesis for quadratic polynomial inequalities and combination with EUF","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Bican Xia, Deepak Kapur, Liyun Dai, Mingshuai Chen, Naijun Zhan, Ting Gan","submitted_at":"2016-01-19T05:05:49Z","abstract_excerpt":"An algorithm for generating interpolants for formulas which are conjunctions of quadratic polynomial inequalities (both strict and nonstrict) is proposed. The algorithm is based on a key observation that quadratic polynomial inequalities can be linearized if they are concave. A generalization of Motzkin's transposition theorem is proved, which is used to generate an interpolant between two mutually contradictory conjunctions of polynomial inequalities, using semi-definite programming in time complexity $\\mathcal{O}(n^3+nm))$, where $n$ is the number of variables and $m$ is the number of inequa"},"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":"1601.04802","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-01-19T05:05:49Z","cross_cats_sorted":[],"title_canon_sha256":"5cd42f5943d9482185cbfce5874556742448d8ba93da87aaac0f3d9848932aad","abstract_canon_sha256":"b052eb0b97458f82fb590a6b46d824eae030ce4ab85eec9212464b2aa5696f05"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:34.618164Z","signature_b64":"jzzjSS3TSrxNMFvwWBSb+Jo9QffyQhQyoiPyEf6tXOAP9Yfi4+AbQx/Np1KTEb4vgjP1P+mMI63cpY73Ck0/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81647c4524bc1d71715e919cf262a71bfe1be8c477457520ed26a4d0a36bbd9b","last_reissued_at":"2026-05-18T00:59:34.617666Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:34.617666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Interpolation synthesis for quadratic polynomial inequalities and combination with EUF","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Bican Xia, Deepak Kapur, Liyun Dai, Mingshuai Chen, Naijun Zhan, Ting Gan","submitted_at":"2016-01-19T05:05:49Z","abstract_excerpt":"An algorithm for generating interpolants for formulas which are conjunctions of quadratic polynomial inequalities (both strict and nonstrict) is proposed. The algorithm is based on a key observation that quadratic polynomial inequalities can be linearized if they are concave. A generalization of Motzkin's transposition theorem is proved, which is used to generate an interpolant between two mutually contradictory conjunctions of polynomial inequalities, using semi-definite programming in time complexity $\\mathcal{O}(n^3+nm))$, where $n$ is the number of variables and $m$ is the number of inequa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04802","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":"1601.04802","created_at":"2026-05-18T00:59:34.617734+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.04802v3","created_at":"2026-05-18T00:59:34.617734+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04802","created_at":"2026-05-18T00:59:34.617734+00:00"},{"alias_kind":"pith_short_12","alias_value":"QFSHYRJEXQOX","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"QFSHYRJEXQOXC4K6","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"QFSHYRJE","created_at":"2026-05-18T12:30:39.010887+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/QFSHYRJEXQOXC4K6SGOPEYVHDP","json":"https://pith.science/pith/QFSHYRJEXQOXC4K6SGOPEYVHDP.json","graph_json":"https://pith.science/api/pith-number/QFSHYRJEXQOXC4K6SGOPEYVHDP/graph.json","events_json":"https://pith.science/api/pith-number/QFSHYRJEXQOXC4K6SGOPEYVHDP/events.json","paper":"https://pith.science/paper/QFSHYRJE"},"agent_actions":{"view_html":"https://pith.science/pith/QFSHYRJEXQOXC4K6SGOPEYVHDP","download_json":"https://pith.science/pith/QFSHYRJEXQOXC4K6SGOPEYVHDP.json","view_paper":"https://pith.science/paper/QFSHYRJE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.04802&json=true","fetch_graph":"https://pith.science/api/pith-number/QFSHYRJEXQOXC4K6SGOPEYVHDP/graph.json","fetch_events":"https://pith.science/api/pith-number/QFSHYRJEXQOXC4K6SGOPEYVHDP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QFSHYRJEXQOXC4K6SGOPEYVHDP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QFSHYRJEXQOXC4K6SGOPEYVHDP/action/storage_attestation","attest_author":"https://pith.science/pith/QFSHYRJEXQOXC4K6SGOPEYVHDP/action/author_attestation","sign_citation":"https://pith.science/pith/QFSHYRJEXQOXC4K6SGOPEYVHDP/action/citation_signature","submit_replication":"https://pith.science/pith/QFSHYRJEXQOXC4K6SGOPEYVHDP/action/replication_record"}},"created_at":"2026-05-18T00:59:34.617734+00:00","updated_at":"2026-05-18T00:59:34.617734+00:00"}