{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6L5VFPSGDRKR45MMSSFX5RYS7G","short_pith_number":"pith:6L5VFPSG","canonical_record":{"source":{"id":"1705.01705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-04T05:09:32Z","cross_cats_sorted":[],"title_canon_sha256":"41caab3fcde493e7b96238689d5949cde5adf4068de7be7e20f3a15b632024cf","abstract_canon_sha256":"d0a2fee7e1a79f9af029f1a1aff75cf107de4f255cb6063b61f85f12486a66c8"},"schema_version":"1.0"},"canonical_sha256":"f2fb52be461c551e758c948b7ec712f9b56dfbcfcc04d812b16d20cca57b0f96","source":{"kind":"arxiv","id":"1705.01705","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01705","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01705v1","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01705","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"pith_short_12","alias_value":"6L5VFPSGDRKR","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6L5VFPSGDRKR45MM","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6L5VFPSG","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6L5VFPSGDRKR45MMSSFX5RYS7G","target":"record","payload":{"canonical_record":{"source":{"id":"1705.01705","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-04T05:09:32Z","cross_cats_sorted":[],"title_canon_sha256":"41caab3fcde493e7b96238689d5949cde5adf4068de7be7e20f3a15b632024cf","abstract_canon_sha256":"d0a2fee7e1a79f9af029f1a1aff75cf107de4f255cb6063b61f85f12486a66c8"},"schema_version":"1.0"},"canonical_sha256":"f2fb52be461c551e758c948b7ec712f9b56dfbcfcc04d812b16d20cca57b0f96","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:04.385434Z","signature_b64":"VgrIvbCf9xMq6Jf2TAtU1187KJXXVffzE3dM5S37p8AnXIk1ebtWbXFlrtZgO7MZ0z6+OUHjiDtFY2gBQJVBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2fb52be461c551e758c948b7ec712f9b56dfbcfcc04d812b16d20cca57b0f96","last_reissued_at":"2026-05-18T00:45:04.385045Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:04.385045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.01705","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:45:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ypPjBE57uUsAaj9D/YYykVBLOyhZngevKytk5tulS0l9K7IPf8J3PwAk/JMx2U+yjwn1DSvQhgBVmD7gNTJQBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:11:48.588511Z"},"content_sha256":"ab1f66d53492785b4382e40735d1d95e9eb0c9f05444e6e59a50110ce6c0e81c","schema_version":"1.0","event_id":"sha256:ab1f66d53492785b4382e40735d1d95e9eb0c9f05444e6e59a50110ce6c0e81c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6L5VFPSGDRKR45MMSSFX5RYS7G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimum Manhattan Distance Approach to Multiple Criteria Decision Making in Multiobjective Optimization Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Gary G. Yen, Teng-Kuei Juan, Wei-Yu Chiu","submitted_at":"2017-05-04T05:09:32Z","abstract_excerpt":"A minimum Manhattan distance (MMD) approach to multiple criteria decision making in multiobjective optimization problems (MOPs) is proposed. The approach selects the final solution corresponding with a vector that has the MMD from a normalized ideal vector. This procedure is equivalent to the knee selection described by a divide and conquer approach that involves iterations of pairwise comparisons. Being able to systematically assign weighting coefficients to multiple criteria, the MMD approach is equivalent to a weighted-sum (WS) approach. Because of the equivalence, the MMD approach possesse"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01705","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:45:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"is/aNQp263f8YszBbaSJWspbllzxd6aXz6b2TPBKrC5QpIew4ICqZBmqmJHBcUtWKzxbmZIJINMkSJUuMqmtDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:11:48.588915Z"},"content_sha256":"6af5635960a74c1182bde827b381e6a380b5fe711578a287fc0a2ffd65fe5ac9","schema_version":"1.0","event_id":"sha256:6af5635960a74c1182bde827b381e6a380b5fe711578a287fc0a2ffd65fe5ac9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6L5VFPSGDRKR45MMSSFX5RYS7G/bundle.json","state_url":"https://pith.science/pith/6L5VFPSGDRKR45MMSSFX5RYS7G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6L5VFPSGDRKR45MMSSFX5RYS7G/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":"2026-06-08T12:11:48Z","links":{"resolver":"https://pith.science/pith/6L5VFPSGDRKR45MMSSFX5RYS7G","bundle":"https://pith.science/pith/6L5VFPSGDRKR45MMSSFX5RYS7G/bundle.json","state":"https://pith.science/pith/6L5VFPSGDRKR45MMSSFX5RYS7G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6L5VFPSGDRKR45MMSSFX5RYS7G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6L5VFPSGDRKR45MMSSFX5RYS7G","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":"d0a2fee7e1a79f9af029f1a1aff75cf107de4f255cb6063b61f85f12486a66c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-04T05:09:32Z","title_canon_sha256":"41caab3fcde493e7b96238689d5949cde5adf4068de7be7e20f3a15b632024cf"},"schema_version":"1.0","source":{"id":"1705.01705","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01705","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01705v1","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01705","created_at":"2026-05-18T00:45:04Z"},{"alias_kind":"pith_short_12","alias_value":"6L5VFPSGDRKR","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6L5VFPSGDRKR45MM","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6L5VFPSG","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:6af5635960a74c1182bde827b381e6a380b5fe711578a287fc0a2ffd65fe5ac9","target":"graph","created_at":"2026-05-18T00:45:04Z","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":"A minimum Manhattan distance (MMD) approach to multiple criteria decision making in multiobjective optimization problems (MOPs) is proposed. The approach selects the final solution corresponding with a vector that has the MMD from a normalized ideal vector. This procedure is equivalent to the knee selection described by a divide and conquer approach that involves iterations of pairwise comparisons. Being able to systematically assign weighting coefficients to multiple criteria, the MMD approach is equivalent to a weighted-sum (WS) approach. Because of the equivalence, the MMD approach possesse","authors_text":"Gary G. Yen, Teng-Kuei Juan, Wei-Yu Chiu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-04T05:09:32Z","title":"Minimum Manhattan Distance Approach to Multiple Criteria Decision Making in Multiobjective Optimization Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01705","kind":"arxiv","version":1},"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:ab1f66d53492785b4382e40735d1d95e9eb0c9f05444e6e59a50110ce6c0e81c","target":"record","created_at":"2026-05-18T00:45:04Z","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":"d0a2fee7e1a79f9af029f1a1aff75cf107de4f255cb6063b61f85f12486a66c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-04T05:09:32Z","title_canon_sha256":"41caab3fcde493e7b96238689d5949cde5adf4068de7be7e20f3a15b632024cf"},"schema_version":"1.0","source":{"id":"1705.01705","kind":"arxiv","version":1}},"canonical_sha256":"f2fb52be461c551e758c948b7ec712f9b56dfbcfcc04d812b16d20cca57b0f96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2fb52be461c551e758c948b7ec712f9b56dfbcfcc04d812b16d20cca57b0f96","first_computed_at":"2026-05-18T00:45:04.385045Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:04.385045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VgrIvbCf9xMq6Jf2TAtU1187KJXXVffzE3dM5S37p8AnXIk1ebtWbXFlrtZgO7MZ0z6+OUHjiDtFY2gBQJVBAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:04.385434Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.01705","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab1f66d53492785b4382e40735d1d95e9eb0c9f05444e6e59a50110ce6c0e81c","sha256:6af5635960a74c1182bde827b381e6a380b5fe711578a287fc0a2ffd65fe5ac9"],"state_sha256":"c90b822e498f3dd6f51f3829c8b08869a5aac3e3eddb7af9e619a423c5322c50"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GMnRuHYucXx+vCkYZHCr41SWTmKaOcDsyKlYFp7CVJnOHw/siN+XLkrpSImrhDla55IcDaOVKKz64mvI4tlNDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T12:11:48.590916Z","bundle_sha256":"4dec73e15270f270d2ec64e22d3ce6bbf774a57f3580917713c8dd4d821f52d5"}}