{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:F44X6U432ACF2LAPHDKAGXUYXX","short_pith_number":"pith:F44X6U43","schema_version":"1.0","canonical_sha256":"2f397f539bd0045d2c0f38d4035e98bde098c738da89f1c8102783e0dfda531b","source":{"kind":"arxiv","id":"2606.26714","version":1},"attestation_state":"computed","paper":{"title":"Random Walk on B\\'ezier Curves for Global Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.NE","authors_text":"Jiguang Yu, Jinpeng Wang, Kaichen Ouyang, Xingguo Xu, Yuansheng Gao, Yujing Sun","submitted_at":"2026-06-25T07:50:06Z","abstract_excerpt":"Balancing exploration and exploitation remains a central challenge in metaheuristic optimization. To address this issue, this paper proposes B\\'ezier Walk Evolution (BWE), a geometry-driven optimization framework that reformulates evolutionary search as adaptive trajectory construction in the decision space. BWE integrates B\\'ezier curve modeling with a distance-aware random walk mechanism to generate topology-guided search trajectories. By adaptively varying the curve order during evolution, the proposed method enables a smooth transition from diversified global exploration to refined local e"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.26714","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2026-06-25T07:50:06Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"5cc0f1faa419874eae23aaa16a21aa4ebbd44a8cf90b0511cf210973117c25e5","abstract_canon_sha256":"24f77084d9e045db15e76fac653cc48308593c6fd6d8153ac441f5c7b55b8873"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-26T01:15:57.757175Z","signature_b64":"pJKpM5n8In5w73WynSLiwCZ8nr/aLZBHYLsqC35Jkpvpnpd2UIVPVQqAejPLasEGSNDxUQcUvYnkXblnZqUrAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f397f539bd0045d2c0f38d4035e98bde098c738da89f1c8102783e0dfda531b","last_reissued_at":"2026-06-26T01:15:57.756778Z","signature_status":"signed_v1","first_computed_at":"2026-06-26T01:15:57.756778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random Walk on B\\'ezier Curves for Global Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.NE","authors_text":"Jiguang Yu, Jinpeng Wang, Kaichen Ouyang, Xingguo Xu, Yuansheng Gao, Yujing Sun","submitted_at":"2026-06-25T07:50:06Z","abstract_excerpt":"Balancing exploration and exploitation remains a central challenge in metaheuristic optimization. To address this issue, this paper proposes B\\'ezier Walk Evolution (BWE), a geometry-driven optimization framework that reformulates evolutionary search as adaptive trajectory construction in the decision space. BWE integrates B\\'ezier curve modeling with a distance-aware random walk mechanism to generate topology-guided search trajectories. By adaptively varying the curve order during evolution, the proposed method enables a smooth transition from diversified global exploration to refined local e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26714","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.26714/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.26714","created_at":"2026-06-26T01:15:57.756834+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.26714v1","created_at":"2026-06-26T01:15:57.756834+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.26714","created_at":"2026-06-26T01:15:57.756834+00:00"},{"alias_kind":"pith_short_12","alias_value":"F44X6U432ACF","created_at":"2026-06-26T01:15:57.756834+00:00"},{"alias_kind":"pith_short_16","alias_value":"F44X6U432ACF2LAP","created_at":"2026-06-26T01:15:57.756834+00:00"},{"alias_kind":"pith_short_8","alias_value":"F44X6U43","created_at":"2026-06-26T01:15:57.756834+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/F44X6U432ACF2LAPHDKAGXUYXX","json":"https://pith.science/pith/F44X6U432ACF2LAPHDKAGXUYXX.json","graph_json":"https://pith.science/api/pith-number/F44X6U432ACF2LAPHDKAGXUYXX/graph.json","events_json":"https://pith.science/api/pith-number/F44X6U432ACF2LAPHDKAGXUYXX/events.json","paper":"https://pith.science/paper/F44X6U43"},"agent_actions":{"view_html":"https://pith.science/pith/F44X6U432ACF2LAPHDKAGXUYXX","download_json":"https://pith.science/pith/F44X6U432ACF2LAPHDKAGXUYXX.json","view_paper":"https://pith.science/paper/F44X6U43","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.26714&json=true","fetch_graph":"https://pith.science/api/pith-number/F44X6U432ACF2LAPHDKAGXUYXX/graph.json","fetch_events":"https://pith.science/api/pith-number/F44X6U432ACF2LAPHDKAGXUYXX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F44X6U432ACF2LAPHDKAGXUYXX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F44X6U432ACF2LAPHDKAGXUYXX/action/storage_attestation","attest_author":"https://pith.science/pith/F44X6U432ACF2LAPHDKAGXUYXX/action/author_attestation","sign_citation":"https://pith.science/pith/F44X6U432ACF2LAPHDKAGXUYXX/action/citation_signature","submit_replication":"https://pith.science/pith/F44X6U432ACF2LAPHDKAGXUYXX/action/replication_record"}},"created_at":"2026-06-26T01:15:57.756834+00:00","updated_at":"2026-06-26T01:15:57.756834+00:00"}