{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ITBSXUWP4T7MCI2SYRBAJ5PCSB","short_pith_number":"pith:ITBSXUWP","canonical_record":{"source":{"id":"1709.10377","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-18T09:59:57Z","cross_cats_sorted":["cs.NE"],"title_canon_sha256":"da4614305554fcdd94cb2ceebc2d4c14f27015bd60af0f89ecd1a9419940496b","abstract_canon_sha256":"14dcc9ca3b7fcaaa61a9595d670196defa0798b6fa4d04756d7970eb068fe406"},"schema_version":"1.0"},"canonical_sha256":"44c32bd2cfe4fec12352c44204f5e2904af690900f16817f04337b46df841912","source":{"kind":"arxiv","id":"1709.10377","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.10377","created_at":"2026-05-18T00:34:01Z"},{"alias_kind":"arxiv_version","alias_value":"1709.10377v1","created_at":"2026-05-18T00:34:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10377","created_at":"2026-05-18T00:34:01Z"},{"alias_kind":"pith_short_12","alias_value":"ITBSXUWP4T7M","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"ITBSXUWP4T7MCI2S","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"ITBSXUWP","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ITBSXUWP4T7MCI2SYRBAJ5PCSB","target":"record","payload":{"canonical_record":{"source":{"id":"1709.10377","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-18T09:59:57Z","cross_cats_sorted":["cs.NE"],"title_canon_sha256":"da4614305554fcdd94cb2ceebc2d4c14f27015bd60af0f89ecd1a9419940496b","abstract_canon_sha256":"14dcc9ca3b7fcaaa61a9595d670196defa0798b6fa4d04756d7970eb068fe406"},"schema_version":"1.0"},"canonical_sha256":"44c32bd2cfe4fec12352c44204f5e2904af690900f16817f04337b46df841912","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:01.263800Z","signature_b64":"zkbfeMLFmCCuMdb0f3ejSyn3VghmsCAsnR0PfIqVW6Wjkf4iak+uJE+8QR0Yg3Uot7hvQBa+GP2sf9gboZx/AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44c32bd2cfe4fec12352c44204f5e2904af690900f16817f04337b46df841912","last_reissued_at":"2026-05-18T00:34:01.263223Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:01.263223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.10377","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":"2026-05-18T00:34:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a7nzomxfUlONQYpnUJNFR0JaDN+dxjsDE0Paw7XTp8B3UbFeue1OpPpc1I9wGxqgcgJm/yg7mw7EMZhj9GdUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:10:30.921078Z"},"content_sha256":"1ab6324db06e37b2e95534887a6d7702e6e8d629f23caf8d54f3a930fc01cc9a","schema_version":"1.0","event_id":"sha256:1ab6324db06e37b2e95534887a6d7702e6e8d629f23caf8d54f3a930fc01cc9a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ITBSXUWP4T7MCI2SYRBAJ5PCSB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simple Problems: The Simplicial Gluing Structure of Pareto Sets and Pareto Fronts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NE"],"primary_cat":"math.OC","authors_text":"Naoki Hamada","submitted_at":"2017-04-18T09:59:57Z","abstract_excerpt":"Quite a few studies on real-world applications of multi-objective optimization reported that their Pareto sets and Pareto fronts form a topological simplex. Such a class of problems was recently named the simple problems, and their Pareto set and Pareto front were observed to have a gluing structure similar to the faces of a simplex. This paper gives a theoretical justification for that observation by proving the gluing structure of the Pareto sets/fronts of subproblems of a simple problem. The simplicity of standard benchmark problems is studied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10377","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":"2026-05-18T00:34:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K/GrrEfktob1IEegMBk72u6kfOU5O4991UL32Q277xZsHcgH/JS3id2p79tSdWnSC73gFQWHWpmK09YY//IvAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:10:30.921432Z"},"content_sha256":"b50cc79787fab92e96ff13a6060df6aaf4c37d3ab6289174c8070e47cf84559c","schema_version":"1.0","event_id":"sha256:b50cc79787fab92e96ff13a6060df6aaf4c37d3ab6289174c8070e47cf84559c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ITBSXUWP4T7MCI2SYRBAJ5PCSB/bundle.json","state_url":"https://pith.science/pith/ITBSXUWP4T7MCI2SYRBAJ5PCSB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ITBSXUWP4T7MCI2SYRBAJ5PCSB/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":"2026-06-25T17:10:30Z","links":{"resolver":"https://pith.science/pith/ITBSXUWP4T7MCI2SYRBAJ5PCSB","bundle":"https://pith.science/pith/ITBSXUWP4T7MCI2SYRBAJ5PCSB/bundle.json","state":"https://pith.science/pith/ITBSXUWP4T7MCI2SYRBAJ5PCSB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ITBSXUWP4T7MCI2SYRBAJ5PCSB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ITBSXUWP4T7MCI2SYRBAJ5PCSB","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":"14dcc9ca3b7fcaaa61a9595d670196defa0798b6fa4d04756d7970eb068fe406","cross_cats_sorted":["cs.NE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-18T09:59:57Z","title_canon_sha256":"da4614305554fcdd94cb2ceebc2d4c14f27015bd60af0f89ecd1a9419940496b"},"schema_version":"1.0","source":{"id":"1709.10377","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.10377","created_at":"2026-05-18T00:34:01Z"},{"alias_kind":"arxiv_version","alias_value":"1709.10377v1","created_at":"2026-05-18T00:34:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10377","created_at":"2026-05-18T00:34:01Z"},{"alias_kind":"pith_short_12","alias_value":"ITBSXUWP4T7M","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"ITBSXUWP4T7MCI2S","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"ITBSXUWP","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:b50cc79787fab92e96ff13a6060df6aaf4c37d3ab6289174c8070e47cf84559c","target":"graph","created_at":"2026-05-18T00:34:01Z","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":"Quite a few studies on real-world applications of multi-objective optimization reported that their Pareto sets and Pareto fronts form a topological simplex. Such a class of problems was recently named the simple problems, and their Pareto set and Pareto front were observed to have a gluing structure similar to the faces of a simplex. This paper gives a theoretical justification for that observation by proving the gluing structure of the Pareto sets/fronts of subproblems of a simple problem. The simplicity of standard benchmark problems is studied.","authors_text":"Naoki Hamada","cross_cats":["cs.NE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-18T09:59:57Z","title":"Simple Problems: The Simplicial Gluing Structure of Pareto Sets and Pareto Fronts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10377","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":"sha256:1ab6324db06e37b2e95534887a6d7702e6e8d629f23caf8d54f3a930fc01cc9a","target":"record","created_at":"2026-05-18T00:34:01Z","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":"14dcc9ca3b7fcaaa61a9595d670196defa0798b6fa4d04756d7970eb068fe406","cross_cats_sorted":["cs.NE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-04-18T09:59:57Z","title_canon_sha256":"da4614305554fcdd94cb2ceebc2d4c14f27015bd60af0f89ecd1a9419940496b"},"schema_version":"1.0","source":{"id":"1709.10377","kind":"arxiv","version":1}},"canonical_sha256":"44c32bd2cfe4fec12352c44204f5e2904af690900f16817f04337b46df841912","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44c32bd2cfe4fec12352c44204f5e2904af690900f16817f04337b46df841912","first_computed_at":"2026-05-18T00:34:01.263223Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:01.263223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zkbfeMLFmCCuMdb0f3ejSyn3VghmsCAsnR0PfIqVW6Wjkf4iak+uJE+8QR0Yg3Uot7hvQBa+GP2sf9gboZx/AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:01.263800Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.10377","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ab6324db06e37b2e95534887a6d7702e6e8d629f23caf8d54f3a930fc01cc9a","sha256:b50cc79787fab92e96ff13a6060df6aaf4c37d3ab6289174c8070e47cf84559c"],"state_sha256":"9ea7756a64de07c34afefb08786d75bc4701e6f0a5961e465bf5c0eda5f19f24"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3ne3NRoQK2NXJuMPaMg99ReRdwopdz2zEduv25WAF3QU0adcYT+nTeemXsw8H72b96Iu0kjtAeC2N+JG4LmTDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T17:10:30.923332Z","bundle_sha256":"945d7deb98ea3f49714a127cbe31e1f5b0366aed18f2ec48d8969609bde82360"}}