{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:G6AZ4TAMYTR5PYTRZLNHMMCCBW","short_pith_number":"pith:G6AZ4TAM","canonical_record":{"source":{"id":"2412.11931","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2024-12-16T16:15:37Z","cross_cats_sorted":[],"title_canon_sha256":"064589ac096ed106a13ac76c909e76db39e68b1b7fb7826b8e59768def1f9c65","abstract_canon_sha256":"e1abf0a659e2448a40a3a379b1a7bcf6899923ab6e3ac5355b9c0a250b8445f9"},"schema_version":"1.0"},"canonical_sha256":"37819e4c0cc4e3d7e271cada7630420dbc03bcb7e07a0037a57387df66971893","source":{"kind":"arxiv","id":"2412.11931","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.11931","created_at":"2026-07-05T10:51:04Z"},{"alias_kind":"arxiv_version","alias_value":"2412.11931v2","created_at":"2026-07-05T10:51:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.11931","created_at":"2026-07-05T10:51:04Z"},{"alias_kind":"pith_short_12","alias_value":"G6AZ4TAMYTR5","created_at":"2026-07-05T10:51:04Z"},{"alias_kind":"pith_short_16","alias_value":"G6AZ4TAMYTR5PYTR","created_at":"2026-07-05T10:51:04Z"},{"alias_kind":"pith_short_8","alias_value":"G6AZ4TAM","created_at":"2026-07-05T10:51:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:G6AZ4TAMYTR5PYTRZLNHMMCCBW","target":"record","payload":{"canonical_record":{"source":{"id":"2412.11931","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2024-12-16T16:15:37Z","cross_cats_sorted":[],"title_canon_sha256":"064589ac096ed106a13ac76c909e76db39e68b1b7fb7826b8e59768def1f9c65","abstract_canon_sha256":"e1abf0a659e2448a40a3a379b1a7bcf6899923ab6e3ac5355b9c0a250b8445f9"},"schema_version":"1.0"},"canonical_sha256":"37819e4c0cc4e3d7e271cada7630420dbc03bcb7e07a0037a57387df66971893","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:51:04.955259Z","signature_b64":"xbQNhUzh4eXtaQl536aGnq484UH9WMYfuOZdOlFaKyB39/GrcinIzahou9HlhknzfuyvNwklX5EFWDhEyH/8AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37819e4c0cc4e3d7e271cada7630420dbc03bcb7e07a0037a57387df66971893","last_reissued_at":"2026-07-05T10:51:04.954720Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:51:04.954720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.11931","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:51:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2tbXczM7EoZSj6B0YeZieo/NMcsb4LsoOqQ8TtagOx4Pb2JmGFNVuN1DNAkTf49P7gUNqqhU9XyPmNwsjITCCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T16:43:59.197739Z"},"content_sha256":"49331e2ab1d8abc3c24576b2bf6b99444a6112278fab38fcf31ebc1a7bdd87e4","schema_version":"1.0","event_id":"sha256:49331e2ab1d8abc3c24576b2bf6b99444a6112278fab38fcf31ebc1a7bdd87e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:G6AZ4TAMYTR5PYTRZLNHMMCCBW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Speeding Up the NSGA-II With a Simple Tie-Breaking Rule","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.NE","authors_text":"Benjamin Doerr, Martin S. Krejca, Tudor Ivan","submitted_at":"2024-12-16T16:15:37Z","abstract_excerpt":"The non-dominated sorting genetic algorithm~II (NSGA-II) is the most popular multi-objective optimization heuristic. Recent mathematical runtime analyses have detected two shortcomings in discrete search spaces, namely, that the NSGA-II has difficulties with more than two objectives and that it is very sensitive to the choice of the population size. To overcome these difficulties, we analyze a simple tie-breaking rule in the selection of the next population. Similar rules have been proposed before, but have found only little acceptance. We prove the effectiveness of our tie-breaking rule via m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.11931","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.11931/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:51:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P9u1B6sa599ueoNXF6FnmowtdpVp82nsLNmzfLZfyTB3cupo8F1QdUy0U887R5MG6vgTULYaCQLyOOASb6I6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T16:43:59.198229Z"},"content_sha256":"bfb4ea21c398f820cc4280ae29862beb81dd02727fe8702e89a20e3e54ac7ace","schema_version":"1.0","event_id":"sha256:bfb4ea21c398f820cc4280ae29862beb81dd02727fe8702e89a20e3e54ac7ace"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G6AZ4TAMYTR5PYTRZLNHMMCCBW/bundle.json","state_url":"https://pith.science/pith/G6AZ4TAMYTR5PYTRZLNHMMCCBW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G6AZ4TAMYTR5PYTRZLNHMMCCBW/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":"2026-08-13T16:43:59Z","links":{"resolver":"https://pith.science/pith/G6AZ4TAMYTR5PYTRZLNHMMCCBW","bundle":"https://pith.science/pith/G6AZ4TAMYTR5PYTRZLNHMMCCBW/bundle.json","state":"https://pith.science/pith/G6AZ4TAMYTR5PYTRZLNHMMCCBW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G6AZ4TAMYTR5PYTRZLNHMMCCBW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:G6AZ4TAMYTR5PYTRZLNHMMCCBW","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":"e1abf0a659e2448a40a3a379b1a7bcf6899923ab6e3ac5355b9c0a250b8445f9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2024-12-16T16:15:37Z","title_canon_sha256":"064589ac096ed106a13ac76c909e76db39e68b1b7fb7826b8e59768def1f9c65"},"schema_version":"1.0","source":{"id":"2412.11931","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.11931","created_at":"2026-07-05T10:51:04Z"},{"alias_kind":"arxiv_version","alias_value":"2412.11931v2","created_at":"2026-07-05T10:51:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.11931","created_at":"2026-07-05T10:51:04Z"},{"alias_kind":"pith_short_12","alias_value":"G6AZ4TAMYTR5","created_at":"2026-07-05T10:51:04Z"},{"alias_kind":"pith_short_16","alias_value":"G6AZ4TAMYTR5PYTR","created_at":"2026-07-05T10:51:04Z"},{"alias_kind":"pith_short_8","alias_value":"G6AZ4TAM","created_at":"2026-07-05T10:51:04Z"}],"graph_snapshots":[{"event_id":"sha256:bfb4ea21c398f820cc4280ae29862beb81dd02727fe8702e89a20e3e54ac7ace","target":"graph","created_at":"2026-07-05T10:51:04Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.11931/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The non-dominated sorting genetic algorithm~II (NSGA-II) is the most popular multi-objective optimization heuristic. Recent mathematical runtime analyses have detected two shortcomings in discrete search spaces, namely, that the NSGA-II has difficulties with more than two objectives and that it is very sensitive to the choice of the population size. To overcome these difficulties, we analyze a simple tie-breaking rule in the selection of the next population. Similar rules have been proposed before, but have found only little acceptance. We prove the effectiveness of our tie-breaking rule via m","authors_text":"Benjamin Doerr, Martin S. Krejca, Tudor Ivan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2024-12-16T16:15:37Z","title":"Speeding Up the NSGA-II With a Simple Tie-Breaking Rule"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.11931","kind":"arxiv","version":2},"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":"sha256:49331e2ab1d8abc3c24576b2bf6b99444a6112278fab38fcf31ebc1a7bdd87e4","target":"record","created_at":"2026-07-05T10:51:04Z","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":"e1abf0a659e2448a40a3a379b1a7bcf6899923ab6e3ac5355b9c0a250b8445f9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2024-12-16T16:15:37Z","title_canon_sha256":"064589ac096ed106a13ac76c909e76db39e68b1b7fb7826b8e59768def1f9c65"},"schema_version":"1.0","source":{"id":"2412.11931","kind":"arxiv","version":2}},"canonical_sha256":"37819e4c0cc4e3d7e271cada7630420dbc03bcb7e07a0037a57387df66971893","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37819e4c0cc4e3d7e271cada7630420dbc03bcb7e07a0037a57387df66971893","first_computed_at":"2026-07-05T10:51:04.954720Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:51:04.954720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xbQNhUzh4eXtaQl536aGnq484UH9WMYfuOZdOlFaKyB39/GrcinIzahou9HlhknzfuyvNwklX5EFWDhEyH/8AA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:51:04.955259Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.11931","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49331e2ab1d8abc3c24576b2bf6b99444a6112278fab38fcf31ebc1a7bdd87e4","sha256:bfb4ea21c398f820cc4280ae29862beb81dd02727fe8702e89a20e3e54ac7ace"],"state_sha256":"fa84ea9e54c93e8c74b25d82dfdac0417b4edfbbb7622dfca4c333784e36593e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P7p4GQGxx0o3N0EICISH4NS3pB8dodhBxIttr5uKr/v7lo/xa1dORu481dm4y3+auQG/kjQK3os6lo0yEM8mCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T16:43:59.203911Z","bundle_sha256":"330024d69329a37cc6e4776302a5e0fdf4c154c424f8208924474e37c3c0d361"}}