{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:RYQV627DNRXH2LBBEXMPQQTV3P","short_pith_number":"pith:RYQV627D","schema_version":"1.0","canonical_sha256":"8e215f6be36c6e7d2c2125d8f84275dbe010e3f528905dfec4be4ca219c6e8bd","source":{"kind":"arxiv","id":"1507.06843","version":2},"attestation_state":"computed","paper":{"title":"A structural geometrical analysis of weakly infeasible SDPs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bruno F. Louren\\c{c}o, Masakazu Muramatsu, Takashi Tsuchiya","submitted_at":"2015-07-24T13:47:02Z","abstract_excerpt":"In this article, we present a geometric theoretical analysis of semidefinite feasibility problems (SDFPs). This is done by decomposing a SDFP into smaller problems, in a way that preserves most feasibility properties of the original problem. With this technique, we develop a detailed analysis of weakly infeasible SDFPs to understand clearly and systematically how weak infeasibility arises in semidefinite programming. In particular, we show that for a weakly infeasible problem over $n\\times n$ matrices, at most $n-1$ directions are required to approach the positive semidefinite cone. We also pr"},"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":"1507.06843","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-07-24T13:47:02Z","cross_cats_sorted":[],"title_canon_sha256":"1ef6412e024df39e8ae8c623903587337082d8f0b9964a3c3340d32674134c5e","abstract_canon_sha256":"a7566869801390023adf715449af0b5c159066197ac4f307e45b1cdf4b6274b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:12.479790Z","signature_b64":"OaT80IhRC/ciHJmlLDlXedXJgvR1jyuB605GYrSuRX0PTrktxXmNamLbLkQtXn5eRXCe4DDjNtWZL2G7a0BdCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e215f6be36c6e7d2c2125d8f84275dbe010e3f528905dfec4be4ca219c6e8bd","last_reissued_at":"2026-05-18T01:36:12.479169Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:12.479169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A structural geometrical analysis of weakly infeasible SDPs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bruno F. Louren\\c{c}o, Masakazu Muramatsu, Takashi Tsuchiya","submitted_at":"2015-07-24T13:47:02Z","abstract_excerpt":"In this article, we present a geometric theoretical analysis of semidefinite feasibility problems (SDFPs). This is done by decomposing a SDFP into smaller problems, in a way that preserves most feasibility properties of the original problem. With this technique, we develop a detailed analysis of weakly infeasible SDFPs to understand clearly and systematically how weak infeasibility arises in semidefinite programming. In particular, we show that for a weakly infeasible problem over $n\\times n$ matrices, at most $n-1$ directions are required to approach the positive semidefinite cone. We also pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06843","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":"1507.06843","created_at":"2026-05-18T01:36:12.479251+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.06843v2","created_at":"2026-05-18T01:36:12.479251+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06843","created_at":"2026-05-18T01:36:12.479251+00:00"},{"alias_kind":"pith_short_12","alias_value":"RYQV627DNRXH","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"RYQV627DNRXH2LBB","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"RYQV627D","created_at":"2026-05-18T12:29:39.896362+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/RYQV627DNRXH2LBBEXMPQQTV3P","json":"https://pith.science/pith/RYQV627DNRXH2LBBEXMPQQTV3P.json","graph_json":"https://pith.science/api/pith-number/RYQV627DNRXH2LBBEXMPQQTV3P/graph.json","events_json":"https://pith.science/api/pith-number/RYQV627DNRXH2LBBEXMPQQTV3P/events.json","paper":"https://pith.science/paper/RYQV627D"},"agent_actions":{"view_html":"https://pith.science/pith/RYQV627DNRXH2LBBEXMPQQTV3P","download_json":"https://pith.science/pith/RYQV627DNRXH2LBBEXMPQQTV3P.json","view_paper":"https://pith.science/paper/RYQV627D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.06843&json=true","fetch_graph":"https://pith.science/api/pith-number/RYQV627DNRXH2LBBEXMPQQTV3P/graph.json","fetch_events":"https://pith.science/api/pith-number/RYQV627DNRXH2LBBEXMPQQTV3P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RYQV627DNRXH2LBBEXMPQQTV3P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RYQV627DNRXH2LBBEXMPQQTV3P/action/storage_attestation","attest_author":"https://pith.science/pith/RYQV627DNRXH2LBBEXMPQQTV3P/action/author_attestation","sign_citation":"https://pith.science/pith/RYQV627DNRXH2LBBEXMPQQTV3P/action/citation_signature","submit_replication":"https://pith.science/pith/RYQV627DNRXH2LBBEXMPQQTV3P/action/replication_record"}},"created_at":"2026-05-18T01:36:12.479251+00:00","updated_at":"2026-05-18T01:36:12.479251+00:00"}