{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DQKV755FGQBU2QVDX36MVSEMKR","short_pith_number":"pith:DQKV755F","canonical_record":{"source":{"id":"1305.5266","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-05-22T20:46:45Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"e14bba7acf8ba947b39f13a4a135d4d177d8651e9689e34693cd46ed50577d25","abstract_canon_sha256":"8121bb0711c892b155588e220574919037f519c2a12d3b69d801ec5e1656e2c6"},"schema_version":"1.0"},"canonical_sha256":"1c155ff7a534034d42a3befccac88c545043d398bf71332512e8243bfc963e40","source":{"kind":"arxiv","id":"1305.5266","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5266","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5266v3","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5266","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"DQKV755FGQBU","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DQKV755FGQBU2QVD","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DQKV755F","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DQKV755FGQBU2QVDX36MVSEMKR","target":"record","payload":{"canonical_record":{"source":{"id":"1305.5266","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-05-22T20:46:45Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"e14bba7acf8ba947b39f13a4a135d4d177d8651e9689e34693cd46ed50577d25","abstract_canon_sha256":"8121bb0711c892b155588e220574919037f519c2a12d3b69d801ec5e1656e2c6"},"schema_version":"1.0"},"canonical_sha256":"1c155ff7a534034d42a3befccac88c545043d398bf71332512e8243bfc963e40","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:31.382451Z","signature_b64":"HcW5yAMWVkCNf85eCxTxhK8KHTxr5GXo/EkWO4uWgPDIHlhEjRLzQZGSKvF4FNPIm/LRYU8+wmdsjMUXSAeICw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c155ff7a534034d42a3befccac88c545043d398bf71332512e8243bfc963e40","last_reissued_at":"2026-05-18T02:46:31.381961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:31.381961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.5266","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NrIlxM+ujIpsw0bAQoPaaSVWoG/VuCmRC1Q8IggiyTuRJvP6mM6Nqiov//dV24b5W8+ny6JAkrLx2RP7FZCHBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T17:08:10.689379Z"},"content_sha256":"ad8d7600ad8f4a0d9067642dc9b3eb82c561decc3d0aece1676f9f17925fe7c0","schema_version":"1.0","event_id":"sha256:ad8d7600ad8f4a0d9067642dc9b3eb82c561decc3d0aece1676f9f17925fe7c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DQKV755FGQBU2QVDX36MVSEMKR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A linear bound on the number of scalarizations needed to solve discrete tricriteria optimization problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.OC","authors_text":"Kathrin Klamroth, Kerstin Daechert","submitted_at":"2013-05-22T20:46:45Z","abstract_excerpt":"General multi-objective optimization problems are often solved by a sequence of parametric single objective problems, so-called scalarizations. If the set of nondominated points is finite, and if an appropriate scalarization is employed, the entire nondominated set can be generated in this way. In the bicriteria case it is well known that this can be realized by an adaptive approach which, given an appropriate initial search space, requires the solution of a number of subproblems which is at most two times the number of nondominated points. For higher dimensional problems, no linear methods we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5266","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qA7/Xdn7yewr9U7rEIfNEdQUSr4toHVtWW0f3AvopUfoqDnPMMXW3M03XEKoQbft00uAPWweIlS5S+Hah9T1Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T17:08:10.690306Z"},"content_sha256":"a6b4f9c78a56d9eb7d8bef3a117b2ba746e1410d0a70d30a8780d63d94ac6fe6","schema_version":"1.0","event_id":"sha256:a6b4f9c78a56d9eb7d8bef3a117b2ba746e1410d0a70d30a8780d63d94ac6fe6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DQKV755FGQBU2QVDX36MVSEMKR/bundle.json","state_url":"https://pith.science/pith/DQKV755FGQBU2QVDX36MVSEMKR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DQKV755FGQBU2QVDX36MVSEMKR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-23T17:08:10Z","links":{"resolver":"https://pith.science/pith/DQKV755FGQBU2QVDX36MVSEMKR","bundle":"https://pith.science/pith/DQKV755FGQBU2QVDX36MVSEMKR/bundle.json","state":"https://pith.science/pith/DQKV755FGQBU2QVDX36MVSEMKR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DQKV755FGQBU2QVDX36MVSEMKR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DQKV755FGQBU2QVDX36MVSEMKR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8121bb0711c892b155588e220574919037f519c2a12d3b69d801ec5e1656e2c6","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-05-22T20:46:45Z","title_canon_sha256":"e14bba7acf8ba947b39f13a4a135d4d177d8651e9689e34693cd46ed50577d25"},"schema_version":"1.0","source":{"id":"1305.5266","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5266","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5266v3","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5266","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"DQKV755FGQBU","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DQKV755FGQBU2QVD","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DQKV755F","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:a6b4f9c78a56d9eb7d8bef3a117b2ba746e1410d0a70d30a8780d63d94ac6fe6","target":"graph","created_at":"2026-05-18T02:46:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"General multi-objective optimization problems are often solved by a sequence of parametric single objective problems, so-called scalarizations. If the set of nondominated points is finite, and if an appropriate scalarization is employed, the entire nondominated set can be generated in this way. In the bicriteria case it is well known that this can be realized by an adaptive approach which, given an appropriate initial search space, requires the solution of a number of subproblems which is at most two times the number of nondominated points. For higher dimensional problems, no linear methods we","authors_text":"Kathrin Klamroth, Kerstin Daechert","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-05-22T20:46:45Z","title":"A linear bound on the number of scalarizations needed to solve discrete tricriteria optimization problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5266","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ad8d7600ad8f4a0d9067642dc9b3eb82c561decc3d0aece1676f9f17925fe7c0","target":"record","created_at":"2026-05-18T02:46:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8121bb0711c892b155588e220574919037f519c2a12d3b69d801ec5e1656e2c6","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-05-22T20:46:45Z","title_canon_sha256":"e14bba7acf8ba947b39f13a4a135d4d177d8651e9689e34693cd46ed50577d25"},"schema_version":"1.0","source":{"id":"1305.5266","kind":"arxiv","version":3}},"canonical_sha256":"1c155ff7a534034d42a3befccac88c545043d398bf71332512e8243bfc963e40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c155ff7a534034d42a3befccac88c545043d398bf71332512e8243bfc963e40","first_computed_at":"2026-05-18T02:46:31.381961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:31.381961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HcW5yAMWVkCNf85eCxTxhK8KHTxr5GXo/EkWO4uWgPDIHlhEjRLzQZGSKvF4FNPIm/LRYU8+wmdsjMUXSAeICw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:31.382451Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.5266","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad8d7600ad8f4a0d9067642dc9b3eb82c561decc3d0aece1676f9f17925fe7c0","sha256:a6b4f9c78a56d9eb7d8bef3a117b2ba746e1410d0a70d30a8780d63d94ac6fe6"],"state_sha256":"6267e141e076958808c2fc3bbc31ae337b82407b034c86fd96a3881139fca9eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0oTWL5dCzoqNf+DjRu0YumCavWnqfKEs61Vlp+UC5lGhtkZu3zGTpSmYtqWWH6ZpIyqbF9pk/rPNsXgiiz9uAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T17:08:10.693791Z","bundle_sha256":"3f6dd08a5d7c7e347691ae848e230ea532a7b9538745c5f2eba1b24dae1ae854"}}