{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:DUTG3XPCEX4YCBCTZALZLB4GQG","short_pith_number":"pith:DUTG3XPC","canonical_record":{"source":{"id":"2109.14195","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2021-09-29T05:15:01Z","cross_cats_sorted":[],"title_canon_sha256":"95d7316ec3cba45afd7bf079f15aeb4b84ba8977e8e9353cf40f2372b46e5030","abstract_canon_sha256":"7e9410cccfec49cead21ddfe37a6a5f700be6ce2fc52e0c337ae9b411b03d412"},"schema_version":"1.0"},"canonical_sha256":"1d266ddde225f9810453c81795878681929c946fb5a20aff403dd9cc5dec1975","source":{"kind":"arxiv","id":"2109.14195","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.14195","created_at":"2026-07-05T04:48:08Z"},{"alias_kind":"arxiv_version","alias_value":"2109.14195v3","created_at":"2026-07-05T04:48:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.14195","created_at":"2026-07-05T04:48:08Z"},{"alias_kind":"pith_short_12","alias_value":"DUTG3XPCEX4Y","created_at":"2026-07-05T04:48:08Z"},{"alias_kind":"pith_short_16","alias_value":"DUTG3XPCEX4YCBCT","created_at":"2026-07-05T04:48:08Z"},{"alias_kind":"pith_short_8","alias_value":"DUTG3XPC","created_at":"2026-07-05T04:48:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:DUTG3XPCEX4YCBCTZALZLB4GQG","target":"record","payload":{"canonical_record":{"source":{"id":"2109.14195","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2021-09-29T05:15:01Z","cross_cats_sorted":[],"title_canon_sha256":"95d7316ec3cba45afd7bf079f15aeb4b84ba8977e8e9353cf40f2372b46e5030","abstract_canon_sha256":"7e9410cccfec49cead21ddfe37a6a5f700be6ce2fc52e0c337ae9b411b03d412"},"schema_version":"1.0"},"canonical_sha256":"1d266ddde225f9810453c81795878681929c946fb5a20aff403dd9cc5dec1975","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:48:08.247093Z","signature_b64":"/jHCLEWFCkLeFUpr2lwFSivfbVU2pqS/sQ00DqYvHqRbjlP0P3nThfMhYlKbtsLIJeyJkSDDTgcSIzlnl0BlBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d266ddde225f9810453c81795878681929c946fb5a20aff403dd9cc5dec1975","last_reissued_at":"2026-07-05T04:48:08.246755Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:48:08.246755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.14195","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":"2026-07-05T04:48:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Is0o1S2Rgg2bHws+zjp+9z5BBGENG1Iwo9oXW1zIAssG/1bb4nhnlhMa3F2oLrhwxSGG7S/+GEztDA0tF2pRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T17:40:26.663868Z"},"content_sha256":"743b0349da91cc83a33257cb18c0d690d31df36ba9f28f9f378ac012ce5cf5cf","schema_version":"1.0","event_id":"sha256:743b0349da91cc83a33257cb18c0d690d31df36ba9f28f9f378ac012ce5cf5cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:DUTG3XPCEX4YCBCTZALZLB4GQG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Influence of Binomial Crossover on Approximation Error of Evolutionary Algorithms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.NE","authors_text":"Cong Wang, Jun He, Xiufen Zou, Yu Chen","submitted_at":"2021-09-29T05:15:01Z","abstract_excerpt":"Although differential evolution (DE) algorithms perform well on a large variety of complicated optimization problems, only a few theoretical studies are focused on the working principle of DE algorithms. To make the first attempt to reveal the function of binomial crossover, this paper aims to answer whether it can reduce the approximation error of evolutionary algorithms. By investigating the expected approximation error and the probability of not finding the optimum, we conduct a case study comparing two evolutionary algorithms with and without binomial crossover on two classical benchmark p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.14195","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2109.14195/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":"2026-07-05T04:48:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cw6RmSq4YWnqWmzzdVaC+UjqaqCTmsnvHd6UvUlwjWPHGpfszQPiIWcXQjz2PZciLfoV80iA3mBdzrBm2lzUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T17:40:26.664370Z"},"content_sha256":"92f268a5bdf8a25bc63c13301ac8aabc41735fcf6e662e3cdb1cc1886bae9e26","schema_version":"1.0","event_id":"sha256:92f268a5bdf8a25bc63c13301ac8aabc41735fcf6e662e3cdb1cc1886bae9e26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DUTG3XPCEX4YCBCTZALZLB4GQG/bundle.json","state_url":"https://pith.science/pith/DUTG3XPCEX4YCBCTZALZLB4GQG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DUTG3XPCEX4YCBCTZALZLB4GQG/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":"2026-08-10T17:40:26Z","links":{"resolver":"https://pith.science/pith/DUTG3XPCEX4YCBCTZALZLB4GQG","bundle":"https://pith.science/pith/DUTG3XPCEX4YCBCTZALZLB4GQG/bundle.json","state":"https://pith.science/pith/DUTG3XPCEX4YCBCTZALZLB4GQG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DUTG3XPCEX4YCBCTZALZLB4GQG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:DUTG3XPCEX4YCBCTZALZLB4GQG","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":"7e9410cccfec49cead21ddfe37a6a5f700be6ce2fc52e0c337ae9b411b03d412","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2021-09-29T05:15:01Z","title_canon_sha256":"95d7316ec3cba45afd7bf079f15aeb4b84ba8977e8e9353cf40f2372b46e5030"},"schema_version":"1.0","source":{"id":"2109.14195","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.14195","created_at":"2026-07-05T04:48:08Z"},{"alias_kind":"arxiv_version","alias_value":"2109.14195v3","created_at":"2026-07-05T04:48:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.14195","created_at":"2026-07-05T04:48:08Z"},{"alias_kind":"pith_short_12","alias_value":"DUTG3XPCEX4Y","created_at":"2026-07-05T04:48:08Z"},{"alias_kind":"pith_short_16","alias_value":"DUTG3XPCEX4YCBCT","created_at":"2026-07-05T04:48:08Z"},{"alias_kind":"pith_short_8","alias_value":"DUTG3XPC","created_at":"2026-07-05T04:48:08Z"}],"graph_snapshots":[{"event_id":"sha256:92f268a5bdf8a25bc63c13301ac8aabc41735fcf6e662e3cdb1cc1886bae9e26","target":"graph","created_at":"2026-07-05T04:48:08Z","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/2109.14195/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Although differential evolution (DE) algorithms perform well on a large variety of complicated optimization problems, only a few theoretical studies are focused on the working principle of DE algorithms. To make the first attempt to reveal the function of binomial crossover, this paper aims to answer whether it can reduce the approximation error of evolutionary algorithms. By investigating the expected approximation error and the probability of not finding the optimum, we conduct a case study comparing two evolutionary algorithms with and without binomial crossover on two classical benchmark p","authors_text":"Cong Wang, Jun He, Xiufen Zou, Yu Chen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2021-09-29T05:15:01Z","title":"Influence of Binomial Crossover on Approximation Error of Evolutionary Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.14195","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":"sha256:743b0349da91cc83a33257cb18c0d690d31df36ba9f28f9f378ac012ce5cf5cf","target":"record","created_at":"2026-07-05T04:48:08Z","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":"7e9410cccfec49cead21ddfe37a6a5f700be6ce2fc52e0c337ae9b411b03d412","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2021-09-29T05:15:01Z","title_canon_sha256":"95d7316ec3cba45afd7bf079f15aeb4b84ba8977e8e9353cf40f2372b46e5030"},"schema_version":"1.0","source":{"id":"2109.14195","kind":"arxiv","version":3}},"canonical_sha256":"1d266ddde225f9810453c81795878681929c946fb5a20aff403dd9cc5dec1975","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d266ddde225f9810453c81795878681929c946fb5a20aff403dd9cc5dec1975","first_computed_at":"2026-07-05T04:48:08.246755Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:48:08.246755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/jHCLEWFCkLeFUpr2lwFSivfbVU2pqS/sQ00DqYvHqRbjlP0P3nThfMhYlKbtsLIJeyJkSDDTgcSIzlnl0BlBA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:48:08.247093Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.14195","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:743b0349da91cc83a33257cb18c0d690d31df36ba9f28f9f378ac012ce5cf5cf","sha256:92f268a5bdf8a25bc63c13301ac8aabc41735fcf6e662e3cdb1cc1886bae9e26"],"state_sha256":"a3b476bb84ccb967204a143cfd23fa68a6f48e911092ba285946bae2f6d27805"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t6iGJktx9J5bRF+BdP+7EKRVu6g9YXnYQAeammBDxyoPz5Z6z5Bmn+1FUd25y97geCynD+D/SZqtqiJekioVCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T17:40:26.670023Z","bundle_sha256":"5063396e46dd72c2f0fadbfcf9889ddf803ab61419518bb35562c0fa30474697"}}