{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:SAJD25RCVYM4LNRKVLVJTOPWWD","short_pith_number":"pith:SAJD25RC","schema_version":"1.0","canonical_sha256":"90123d7622ae19c5b62aaaea99b9f6b0c0d98796d3faf425b6b124afe92f2371","source":{"kind":"arxiv","id":"1707.06712","version":2},"attestation_state":"computed","paper":{"title":"Facets of a mixed-integer bilinear covering set with bounds on variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Ashutosh Mahajan, Hamidur Rahman","submitted_at":"2017-07-20T21:53:55Z","abstract_excerpt":"We derive a closed form description of the convex hull of mixed-integer bilinear covering set with bounds on the integer variables. This convex hull description is determined by considering some orthogonal disjunctive sets defined in a certain way. This description does not introduce any new variables, but consists of exponentially many inequalities. An extended formulation with a few extra variables and much smaller number of constraints is presented. We also derive a linear time separation algorithm for finding the facet defining inequalities of this convex hull. We study the effectiveness o"},"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":"1707.06712","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-07-20T21:53:55Z","cross_cats_sorted":[],"title_canon_sha256":"9ef30c963eb20d7cd718e824ca6c9ff3ae6075b1ca9764c280a1a945952f3804","abstract_canon_sha256":"ac3e3854426e6e2b1a81010c0d83c74a1edf178f9f78fcf0b946269f7a1dff81"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:18.957770Z","signature_b64":"iPp4Ka0fZkzNGmcTYxGB6ywTTfx7TO4EOe6DWRA/FbBe7E+h3wb+KdWrUrGKztk6qzQDC6p6Ep+F7QYmAdGsBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90123d7622ae19c5b62aaaea99b9f6b0c0d98796d3faf425b6b124afe92f2371","last_reissued_at":"2026-05-17T23:52:18.957194Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:18.957194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Facets of a mixed-integer bilinear covering set with bounds on variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Ashutosh Mahajan, Hamidur Rahman","submitted_at":"2017-07-20T21:53:55Z","abstract_excerpt":"We derive a closed form description of the convex hull of mixed-integer bilinear covering set with bounds on the integer variables. This convex hull description is determined by considering some orthogonal disjunctive sets defined in a certain way. This description does not introduce any new variables, but consists of exponentially many inequalities. An extended formulation with a few extra variables and much smaller number of constraints is presented. We also derive a linear time separation algorithm for finding the facet defining inequalities of this convex hull. We study the effectiveness o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06712","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":"1707.06712","created_at":"2026-05-17T23:52:18.957288+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.06712v2","created_at":"2026-05-17T23:52:18.957288+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06712","created_at":"2026-05-17T23:52:18.957288+00:00"},{"alias_kind":"pith_short_12","alias_value":"SAJD25RCVYM4","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"SAJD25RCVYM4LNRK","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"SAJD25RC","created_at":"2026-05-18T12:31:43.269735+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/SAJD25RCVYM4LNRKVLVJTOPWWD","json":"https://pith.science/pith/SAJD25RCVYM4LNRKVLVJTOPWWD.json","graph_json":"https://pith.science/api/pith-number/SAJD25RCVYM4LNRKVLVJTOPWWD/graph.json","events_json":"https://pith.science/api/pith-number/SAJD25RCVYM4LNRKVLVJTOPWWD/events.json","paper":"https://pith.science/paper/SAJD25RC"},"agent_actions":{"view_html":"https://pith.science/pith/SAJD25RCVYM4LNRKVLVJTOPWWD","download_json":"https://pith.science/pith/SAJD25RCVYM4LNRKVLVJTOPWWD.json","view_paper":"https://pith.science/paper/SAJD25RC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.06712&json=true","fetch_graph":"https://pith.science/api/pith-number/SAJD25RCVYM4LNRKVLVJTOPWWD/graph.json","fetch_events":"https://pith.science/api/pith-number/SAJD25RCVYM4LNRKVLVJTOPWWD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SAJD25RCVYM4LNRKVLVJTOPWWD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SAJD25RCVYM4LNRKVLVJTOPWWD/action/storage_attestation","attest_author":"https://pith.science/pith/SAJD25RCVYM4LNRKVLVJTOPWWD/action/author_attestation","sign_citation":"https://pith.science/pith/SAJD25RCVYM4LNRKVLVJTOPWWD/action/citation_signature","submit_replication":"https://pith.science/pith/SAJD25RCVYM4LNRKVLVJTOPWWD/action/replication_record"}},"created_at":"2026-05-17T23:52:18.957288+00:00","updated_at":"2026-05-17T23:52:18.957288+00:00"}