{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:5FGS5B3A57RHWLQIAJCMEXIBME","short_pith_number":"pith:5FGS5B3A","schema_version":"1.0","canonical_sha256":"e94d2e8760efe27b2e080244c25d0161297262af810400ccf95ef1444bce45b8","source":{"kind":"arxiv","id":"1603.08370","version":2},"attestation_state":"computed","paper":{"title":"The Signed Positive Semidefinite Matrix Completion Problem for Odd-$K_4$ Minor Free Signed Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.CO","authors_text":"Shin-ichi Tanigawa","submitted_at":"2016-03-28T12:25:44Z","abstract_excerpt":"We give a signed generalization of Laurent's theorem that characterizes feasible positive semidefinite matrix completion problems in terms of metric polytopes. Based on this result, we give a characterization of the maximum rank completions of the signed positive semidefinite matrix completion problem for odd-$K_4$ minor free signed graphs. The analysis can also be used to bound the minimum rank over the completions and to characterize uniquely solvable completion problems for odd-$K_4$ minor free signed graphs. As a corollary we derive a characterization of the universal rigidity of odd-$K_4$"},"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":"1603.08370","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-28T12:25:44Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"53b3e6684082a8359bcf6246ee767804f17752e0e524421715bcb4f1302b0eef","abstract_canon_sha256":"21dd7d80cf9f76668f8f5e1c49b1b2be9789616e8b18e1fb94f922c7038ba2c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:54.970016Z","signature_b64":"J9VT/VoVioGxx4HIQt72GABmLnaZJJlainnNrfC6n0oBCGxZ79VVl1ASGeKKXVGcypFPHlWlR6fuXF9MLX6HBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e94d2e8760efe27b2e080244c25d0161297262af810400ccf95ef1444bce45b8","last_reissued_at":"2026-05-18T01:17:54.969294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:54.969294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Signed Positive Semidefinite Matrix Completion Problem for Odd-$K_4$ Minor Free Signed Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.CO","authors_text":"Shin-ichi Tanigawa","submitted_at":"2016-03-28T12:25:44Z","abstract_excerpt":"We give a signed generalization of Laurent's theorem that characterizes feasible positive semidefinite matrix completion problems in terms of metric polytopes. Based on this result, we give a characterization of the maximum rank completions of the signed positive semidefinite matrix completion problem for odd-$K_4$ minor free signed graphs. The analysis can also be used to bound the minimum rank over the completions and to characterize uniquely solvable completion problems for odd-$K_4$ minor free signed graphs. As a corollary we derive a characterization of the universal rigidity of odd-$K_4$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08370","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":"1603.08370","created_at":"2026-05-18T01:17:54.969407+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.08370v2","created_at":"2026-05-18T01:17:54.969407+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08370","created_at":"2026-05-18T01:17:54.969407+00:00"},{"alias_kind":"pith_short_12","alias_value":"5FGS5B3A57RH","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"5FGS5B3A57RHWLQI","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"5FGS5B3A","created_at":"2026-05-18T12:30:01.593930+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/5FGS5B3A57RHWLQIAJCMEXIBME","json":"https://pith.science/pith/5FGS5B3A57RHWLQIAJCMEXIBME.json","graph_json":"https://pith.science/api/pith-number/5FGS5B3A57RHWLQIAJCMEXIBME/graph.json","events_json":"https://pith.science/api/pith-number/5FGS5B3A57RHWLQIAJCMEXIBME/events.json","paper":"https://pith.science/paper/5FGS5B3A"},"agent_actions":{"view_html":"https://pith.science/pith/5FGS5B3A57RHWLQIAJCMEXIBME","download_json":"https://pith.science/pith/5FGS5B3A57RHWLQIAJCMEXIBME.json","view_paper":"https://pith.science/paper/5FGS5B3A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.08370&json=true","fetch_graph":"https://pith.science/api/pith-number/5FGS5B3A57RHWLQIAJCMEXIBME/graph.json","fetch_events":"https://pith.science/api/pith-number/5FGS5B3A57RHWLQIAJCMEXIBME/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5FGS5B3A57RHWLQIAJCMEXIBME/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5FGS5B3A57RHWLQIAJCMEXIBME/action/storage_attestation","attest_author":"https://pith.science/pith/5FGS5B3A57RHWLQIAJCMEXIBME/action/author_attestation","sign_citation":"https://pith.science/pith/5FGS5B3A57RHWLQIAJCMEXIBME/action/citation_signature","submit_replication":"https://pith.science/pith/5FGS5B3A57RHWLQIAJCMEXIBME/action/replication_record"}},"created_at":"2026-05-18T01:17:54.969407+00:00","updated_at":"2026-05-18T01:17:54.969407+00:00"}