{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:AOJTWGRYG3VATIUHMQBXBZGLW6","short_pith_number":"pith:AOJTWGRY","schema_version":"1.0","canonical_sha256":"03933b1a3836ea09a287640370e4cbb7b6a0363f412b7028081a927f04fb89bc","source":{"kind":"arxiv","id":"1108.0760","version":1},"attestation_state":"computed","paper":{"title":"A Complementarity Partition Theorem for Multifold Conic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Javier Pe\\~na, Vera Roshchina","submitted_at":"2011-08-03T06:52:10Z","abstract_excerpt":"Consider a homogeneous multifold convex conic system $$ Ax = 0, \\; x\\in K_1\\times...\\times K_r $$ and its alternative system $$ A\\transp y \\in K_1^*\\times...\\times K_r^*, $$ where $K_1,..., K_r$ are regular closed convex cones. We show that there is canonical partition of the index set ${1,...,r}$ determined by certain complementarity sets associated to the most interior solutions to the two systems. Our results are inspired by and extend the Goldman-Tucker Theorem for linear programming."},"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":"1108.0760","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-08-03T06:52:10Z","cross_cats_sorted":[],"title_canon_sha256":"2691aa86ff5fb37284baeaa61901a18e2365cabaf91826cd1218a860fee4bff1","abstract_canon_sha256":"fea5a773cd8a7ae9dfdf1186c3f854db2816fb85db150d5f064b8541facc7f18"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:22.026706Z","signature_b64":"LZDY462NMmC/lSHRUuKYChh7w5LGTO7/lHHnjLo1cFww7cC/OwhfahM/K1KOrgDGpk5rhyPncAad/vU8oxKNDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03933b1a3836ea09a287640370e4cbb7b6a0363f412b7028081a927f04fb89bc","last_reissued_at":"2026-05-18T04:16:22.026088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:22.026088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Complementarity Partition Theorem for Multifold Conic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Javier Pe\\~na, Vera Roshchina","submitted_at":"2011-08-03T06:52:10Z","abstract_excerpt":"Consider a homogeneous multifold convex conic system $$ Ax = 0, \\; x\\in K_1\\times...\\times K_r $$ and its alternative system $$ A\\transp y \\in K_1^*\\times...\\times K_r^*, $$ where $K_1,..., K_r$ are regular closed convex cones. We show that there is canonical partition of the index set ${1,...,r}$ determined by certain complementarity sets associated to the most interior solutions to the two systems. Our results are inspired by and extend the Goldman-Tucker Theorem for linear programming."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0760","kind":"arxiv","version":1},"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":"1108.0760","created_at":"2026-05-18T04:16:22.026176+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.0760v1","created_at":"2026-05-18T04:16:22.026176+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0760","created_at":"2026-05-18T04:16:22.026176+00:00"},{"alias_kind":"pith_short_12","alias_value":"AOJTWGRYG3VA","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"AOJTWGRYG3VATIUH","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"AOJTWGRY","created_at":"2026-05-18T12:26:24.575870+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/AOJTWGRYG3VATIUHMQBXBZGLW6","json":"https://pith.science/pith/AOJTWGRYG3VATIUHMQBXBZGLW6.json","graph_json":"https://pith.science/api/pith-number/AOJTWGRYG3VATIUHMQBXBZGLW6/graph.json","events_json":"https://pith.science/api/pith-number/AOJTWGRYG3VATIUHMQBXBZGLW6/events.json","paper":"https://pith.science/paper/AOJTWGRY"},"agent_actions":{"view_html":"https://pith.science/pith/AOJTWGRYG3VATIUHMQBXBZGLW6","download_json":"https://pith.science/pith/AOJTWGRYG3VATIUHMQBXBZGLW6.json","view_paper":"https://pith.science/paper/AOJTWGRY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.0760&json=true","fetch_graph":"https://pith.science/api/pith-number/AOJTWGRYG3VATIUHMQBXBZGLW6/graph.json","fetch_events":"https://pith.science/api/pith-number/AOJTWGRYG3VATIUHMQBXBZGLW6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AOJTWGRYG3VATIUHMQBXBZGLW6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AOJTWGRYG3VATIUHMQBXBZGLW6/action/storage_attestation","attest_author":"https://pith.science/pith/AOJTWGRYG3VATIUHMQBXBZGLW6/action/author_attestation","sign_citation":"https://pith.science/pith/AOJTWGRYG3VATIUHMQBXBZGLW6/action/citation_signature","submit_replication":"https://pith.science/pith/AOJTWGRYG3VATIUHMQBXBZGLW6/action/replication_record"}},"created_at":"2026-05-18T04:16:22.026176+00:00","updated_at":"2026-05-18T04:16:22.026176+00:00"}