{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:VA6LFCOI2EVDIUWPC6XEJ54RZC","short_pith_number":"pith:VA6LFCOI","canonical_record":{"source":{"id":"2501.08906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-01-15T16:15:29Z","cross_cats_sorted":[],"title_canon_sha256":"cd387248db014f10f806f1bdb79fb6a5c123bbd67969e9fc0902c6909e954ba6","abstract_canon_sha256":"48e1fb94415d57f505d5d35ac87a7c022754705018fe10916716b7a06970043e"},"schema_version":"1.0"},"canonical_sha256":"a83cb289c8d12a3452cf17ae44f791c881db8cf516eda91b69f609beccc2061e","source":{"kind":"arxiv","id":"2501.08906","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.08906","created_at":"2026-07-05T10:01:27Z"},{"alias_kind":"arxiv_version","alias_value":"2501.08906v1","created_at":"2026-07-05T10:01:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.08906","created_at":"2026-07-05T10:01:27Z"},{"alias_kind":"pith_short_12","alias_value":"VA6LFCOI2EVD","created_at":"2026-07-05T10:01:27Z"},{"alias_kind":"pith_short_16","alias_value":"VA6LFCOI2EVDIUWP","created_at":"2026-07-05T10:01:27Z"},{"alias_kind":"pith_short_8","alias_value":"VA6LFCOI","created_at":"2026-07-05T10:01:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:VA6LFCOI2EVDIUWPC6XEJ54RZC","target":"record","payload":{"canonical_record":{"source":{"id":"2501.08906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-01-15T16:15:29Z","cross_cats_sorted":[],"title_canon_sha256":"cd387248db014f10f806f1bdb79fb6a5c123bbd67969e9fc0902c6909e954ba6","abstract_canon_sha256":"48e1fb94415d57f505d5d35ac87a7c022754705018fe10916716b7a06970043e"},"schema_version":"1.0"},"canonical_sha256":"a83cb289c8d12a3452cf17ae44f791c881db8cf516eda91b69f609beccc2061e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:01:27.754368Z","signature_b64":"VorPlYo+N2UDKvTpeIHdE0gTJztYiyFqzOWlCi5x7kVfkQVxG48UIOaTeOnF8h86zcvedpgE1GP9zTGnRxRcAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a83cb289c8d12a3452cf17ae44f791c881db8cf516eda91b69f609beccc2061e","last_reissued_at":"2026-07-05T10:01:27.753854Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:01:27.753854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.08906","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":"2026-07-05T10:01:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qc2T8lE5HEU86z59zePRvWdFOTiFM6gE2Azgp6kHLNysz8t18yvixeZo/jkjfZzsh8dbwyFGQZ2clvGrIz+0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T07:14:52.070568Z"},"content_sha256":"f4561bb403f38b09906563f70b43bb6b1d035da56a27dc84482c1c82abeaaec1","schema_version":"1.0","event_id":"sha256:f4561bb403f38b09906563f70b43bb6b1d035da56a27dc84482c1c82abeaaec1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:VA6LFCOI2EVDIUWPC6XEJ54RZC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A consensus-based optimization method for nonsmooth nonconvex programs with approximated gradient descent scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Fan Wu, Jiazhen Wei, Wei Bian","submitted_at":"2025-01-15T16:15:29Z","abstract_excerpt":"In this paper, we are interested in finding the global minimizer of a nonsmooth nonconvex unconstrained optimization problem. By combining the discrete consensus-based optimization (CBO) algorithm and the gradient descent method, we develop a novel CBO algorithm with an extra gradient descent scheme evaluated by the forward-difference technique on the function values, where only the objective function values are used in the proposed algorithm. First, we prove that the proposed algorithm can exhibit global consensus in an exponential rate in two senses and possess a unique global consensus poin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.08906","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/2501.08906/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":"2026-07-05T10:01:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AX7c+aDuyv49sW6rHApLuEHkij0B4a5eAdGj/0qwgv0CL2S1PyJBa04y2811piVkvBpH9hSIT55xZbVcMr3aCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T07:14:52.071054Z"},"content_sha256":"9c6e9e6ddfa4dcad59c134bfe1b4438d94ce7ea73eae3abcb1d25462809a119a","schema_version":"1.0","event_id":"sha256:9c6e9e6ddfa4dcad59c134bfe1b4438d94ce7ea73eae3abcb1d25462809a119a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VA6LFCOI2EVDIUWPC6XEJ54RZC/bundle.json","state_url":"https://pith.science/pith/VA6LFCOI2EVDIUWPC6XEJ54RZC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VA6LFCOI2EVDIUWPC6XEJ54RZC/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":"2026-08-06T07:14:52Z","links":{"resolver":"https://pith.science/pith/VA6LFCOI2EVDIUWPC6XEJ54RZC","bundle":"https://pith.science/pith/VA6LFCOI2EVDIUWPC6XEJ54RZC/bundle.json","state":"https://pith.science/pith/VA6LFCOI2EVDIUWPC6XEJ54RZC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VA6LFCOI2EVDIUWPC6XEJ54RZC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:VA6LFCOI2EVDIUWPC6XEJ54RZC","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":"48e1fb94415d57f505d5d35ac87a7c022754705018fe10916716b7a06970043e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-01-15T16:15:29Z","title_canon_sha256":"cd387248db014f10f806f1bdb79fb6a5c123bbd67969e9fc0902c6909e954ba6"},"schema_version":"1.0","source":{"id":"2501.08906","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.08906","created_at":"2026-07-05T10:01:27Z"},{"alias_kind":"arxiv_version","alias_value":"2501.08906v1","created_at":"2026-07-05T10:01:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.08906","created_at":"2026-07-05T10:01:27Z"},{"alias_kind":"pith_short_12","alias_value":"VA6LFCOI2EVD","created_at":"2026-07-05T10:01:27Z"},{"alias_kind":"pith_short_16","alias_value":"VA6LFCOI2EVDIUWP","created_at":"2026-07-05T10:01:27Z"},{"alias_kind":"pith_short_8","alias_value":"VA6LFCOI","created_at":"2026-07-05T10:01:27Z"}],"graph_snapshots":[{"event_id":"sha256:9c6e9e6ddfa4dcad59c134bfe1b4438d94ce7ea73eae3abcb1d25462809a119a","target":"graph","created_at":"2026-07-05T10:01:27Z","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/2501.08906/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we are interested in finding the global minimizer of a nonsmooth nonconvex unconstrained optimization problem. By combining the discrete consensus-based optimization (CBO) algorithm and the gradient descent method, we develop a novel CBO algorithm with an extra gradient descent scheme evaluated by the forward-difference technique on the function values, where only the objective function values are used in the proposed algorithm. First, we prove that the proposed algorithm can exhibit global consensus in an exponential rate in two senses and possess a unique global consensus poin","authors_text":"Fan Wu, Jiazhen Wei, Wei Bian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-01-15T16:15:29Z","title":"A consensus-based optimization method for nonsmooth nonconvex programs with approximated gradient descent scheme"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.08906","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:f4561bb403f38b09906563f70b43bb6b1d035da56a27dc84482c1c82abeaaec1","target":"record","created_at":"2026-07-05T10:01:27Z","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":"48e1fb94415d57f505d5d35ac87a7c022754705018fe10916716b7a06970043e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-01-15T16:15:29Z","title_canon_sha256":"cd387248db014f10f806f1bdb79fb6a5c123bbd67969e9fc0902c6909e954ba6"},"schema_version":"1.0","source":{"id":"2501.08906","kind":"arxiv","version":1}},"canonical_sha256":"a83cb289c8d12a3452cf17ae44f791c881db8cf516eda91b69f609beccc2061e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a83cb289c8d12a3452cf17ae44f791c881db8cf516eda91b69f609beccc2061e","first_computed_at":"2026-07-05T10:01:27.753854Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:01:27.753854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VorPlYo+N2UDKvTpeIHdE0gTJztYiyFqzOWlCi5x7kVfkQVxG48UIOaTeOnF8h86zcvedpgE1GP9zTGnRxRcAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:01:27.754368Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.08906","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4561bb403f38b09906563f70b43bb6b1d035da56a27dc84482c1c82abeaaec1","sha256:9c6e9e6ddfa4dcad59c134bfe1b4438d94ce7ea73eae3abcb1d25462809a119a"],"state_sha256":"9683e7eed7aeb7963fc46043b9a8d30c653f3aa855fd18fdc77c331307d88892"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i2rRDo6nR3m1KqevBMYxxrXb3BIQ7FT8+9xGg92kx9sX2gr6L3rFzLS38TtS9XZ0SL1RjL74+Rt+YfEb+DokCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T07:14:52.074396Z","bundle_sha256":"25c4a3cbc8f8ab075f5044158cde8935d19ded1916c5ef82903fe2eadd208226"}}