{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UZTEDI7BVL446E6QXHXU4E3IHL","short_pith_number":"pith:UZTEDI7B","schema_version":"1.0","canonical_sha256":"a66641a3e1aaf9cf13d0b9ef4e13683ac1bf910f790967bb983f8866123ff89d","source":{"kind":"arxiv","id":"1504.02602","version":4},"attestation_state":"computed","paper":{"title":"Algebraic solution of tropical optimization problems via matrix sparsification with application to scheduling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"math.OC","authors_text":"Nikolai Krivulin","submitted_at":"2015-04-10T09:20:46Z","abstract_excerpt":"Optimization problems are considered in the framework of tropical algebra to minimize and maximize a nonlinear objective function defined on vectors over an idempotent semifield, and calculated using multiplicative conjugate transposition. To find the minimum of the function, we first obtain a partial solution, which explicitly represents a subset of solution vectors. We characterize all solutions by a system of simultaneous equation and inequality, and show that the solution set is closed under vector addition and scalar multiplication. A matrix sparsification technique is proposed to extend "},"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":"1504.02602","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-04-10T09:20:46Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"61d69fe1d0d78fa954e1fbcac65415d9cfac29f5a46b9545651b478693dff554","abstract_canon_sha256":"e5731d6d8fa34d4c1d7ffd50e605e60819e4cbe8dcd6d1c7c2f53ee7c83c4bf5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:13.600210Z","signature_b64":"jwOflSIBgsDRBLtz9BsP3/lhkWGue0ClpYAnDeNhRX91cHxDvNPo3/IDKweSB39dDKbjm/FDXmuMfK3X6x8BBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a66641a3e1aaf9cf13d0b9ef4e13683ac1bf910f790967bb983f8866123ff89d","last_reissued_at":"2026-05-18T00:43:13.599450Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:13.599450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic solution of tropical optimization problems via matrix sparsification with application to scheduling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"math.OC","authors_text":"Nikolai Krivulin","submitted_at":"2015-04-10T09:20:46Z","abstract_excerpt":"Optimization problems are considered in the framework of tropical algebra to minimize and maximize a nonlinear objective function defined on vectors over an idempotent semifield, and calculated using multiplicative conjugate transposition. To find the minimum of the function, we first obtain a partial solution, which explicitly represents a subset of solution vectors. We characterize all solutions by a system of simultaneous equation and inequality, and show that the solution set is closed under vector addition and scalar multiplication. A matrix sparsification technique is proposed to extend "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02602","kind":"arxiv","version":4},"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":"1504.02602","created_at":"2026-05-18T00:43:13.599586+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.02602v4","created_at":"2026-05-18T00:43:13.599586+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02602","created_at":"2026-05-18T00:43:13.599586+00:00"},{"alias_kind":"pith_short_12","alias_value":"UZTEDI7BVL44","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UZTEDI7BVL446E6Q","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UZTEDI7B","created_at":"2026-05-18T12:29:44.643036+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/UZTEDI7BVL446E6QXHXU4E3IHL","json":"https://pith.science/pith/UZTEDI7BVL446E6QXHXU4E3IHL.json","graph_json":"https://pith.science/api/pith-number/UZTEDI7BVL446E6QXHXU4E3IHL/graph.json","events_json":"https://pith.science/api/pith-number/UZTEDI7BVL446E6QXHXU4E3IHL/events.json","paper":"https://pith.science/paper/UZTEDI7B"},"agent_actions":{"view_html":"https://pith.science/pith/UZTEDI7BVL446E6QXHXU4E3IHL","download_json":"https://pith.science/pith/UZTEDI7BVL446E6QXHXU4E3IHL.json","view_paper":"https://pith.science/paper/UZTEDI7B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.02602&json=true","fetch_graph":"https://pith.science/api/pith-number/UZTEDI7BVL446E6QXHXU4E3IHL/graph.json","fetch_events":"https://pith.science/api/pith-number/UZTEDI7BVL446E6QXHXU4E3IHL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UZTEDI7BVL446E6QXHXU4E3IHL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UZTEDI7BVL446E6QXHXU4E3IHL/action/storage_attestation","attest_author":"https://pith.science/pith/UZTEDI7BVL446E6QXHXU4E3IHL/action/author_attestation","sign_citation":"https://pith.science/pith/UZTEDI7BVL446E6QXHXU4E3IHL/action/citation_signature","submit_replication":"https://pith.science/pith/UZTEDI7BVL446E6QXHXU4E3IHL/action/replication_record"}},"created_at":"2026-05-18T00:43:13.599586+00:00","updated_at":"2026-05-18T00:43:13.599586+00:00"}