{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:O3AY3JOTSKKRLLPFWXP2GCFCTB","short_pith_number":"pith:O3AY3JOT","canonical_record":{"source":{"id":"2011.10778","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-11-21T11:48:07Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"60cd1769d21dad267a90c6a85fe576a4449ef6f0684ceac137774ef2589b04d3","abstract_canon_sha256":"6ef567eed86b08e98487441ab7aed8c2eabb19feba02093fe6cd745615818bc0"},"schema_version":"1.0"},"canonical_sha256":"76c18da5d3929515ade5b5dfa308a2987bfeb08287ba690188393b53ce559446","source":{"kind":"arxiv","id":"2011.10778","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.10778","created_at":"2026-07-05T01:56:16Z"},{"alias_kind":"arxiv_version","alias_value":"2011.10778v1","created_at":"2026-07-05T01:56:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.10778","created_at":"2026-07-05T01:56:16Z"},{"alias_kind":"pith_short_12","alias_value":"O3AY3JOTSKKR","created_at":"2026-07-05T01:56:16Z"},{"alias_kind":"pith_short_16","alias_value":"O3AY3JOTSKKRLLPF","created_at":"2026-07-05T01:56:16Z"},{"alias_kind":"pith_short_8","alias_value":"O3AY3JOT","created_at":"2026-07-05T01:56:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:O3AY3JOTSKKRLLPFWXP2GCFCTB","target":"record","payload":{"canonical_record":{"source":{"id":"2011.10778","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-11-21T11:48:07Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"60cd1769d21dad267a90c6a85fe576a4449ef6f0684ceac137774ef2589b04d3","abstract_canon_sha256":"6ef567eed86b08e98487441ab7aed8c2eabb19feba02093fe6cd745615818bc0"},"schema_version":"1.0"},"canonical_sha256":"76c18da5d3929515ade5b5dfa308a2987bfeb08287ba690188393b53ce559446","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:56:16.098092Z","signature_b64":"q2O9bAqvjgcjlBIpIwFLCZVgi/OC6IE4KyD9C1k5pNHT4fHDYnoQlVwmewOGIXGXxj8Fy0F4/nEnDnzsQnOzDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76c18da5d3929515ade5b5dfa308a2987bfeb08287ba690188393b53ce559446","last_reissued_at":"2026-07-05T01:56:16.097673Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:56:16.097673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2011.10778","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":"2026-07-05T01:56:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WBAsaCx/t1aTsI+9WQkwRjjxZVrsPAn+4yaP8A1H4sKpE+NTJpRsz2G9G5mShutpGpMVHcrEvdeefEhRvFjLCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-17T17:31:52.185568Z"},"content_sha256":"c0b64713b02b6e8386ed8db4ffb54c8ced2dc9e967d714d78f9ac4c1283371b9","schema_version":"1.0","event_id":"sha256:c0b64713b02b6e8386ed8db4ffb54c8ced2dc9e967d714d78f9ac4c1283371b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:O3AY3JOTSKKRLLPFWXP2GCFCTB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Random Batch Method for second order interacting particle systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Lei Li, Shi Jin, Yiqun Sun","submitted_at":"2020-11-21T11:48:07Z","abstract_excerpt":"We investigate several important issues regarding the Random Batch Method (RBM) for second order interacting particle systems. We first show the uniform-in-time strong convergence for second order systems under suitable contraction conditions. Secondly, we propose the application of RBM for singular interaction kernels via kernel splitting strategy, and investigate numerically the application to molecular dynamics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.10778","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/2011.10778/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":"2026-07-05T01:56:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6lWldcmxkQSZgL+bMHVBgOS85RcSkQHSFXddZxOJtbtMARmpvPZTiJOgU7D6hLiBvyF8a0G0wuev1bQHlVI2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-17T17:31:52.185960Z"},"content_sha256":"0996dea37c2a7a7d85b4f1dd2d371f1b807141a8e926c79ba95a9d631237f950","schema_version":"1.0","event_id":"sha256:0996dea37c2a7a7d85b4f1dd2d371f1b807141a8e926c79ba95a9d631237f950"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O3AY3JOTSKKRLLPFWXP2GCFCTB/bundle.json","state_url":"https://pith.science/pith/O3AY3JOTSKKRLLPFWXP2GCFCTB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O3AY3JOTSKKRLLPFWXP2GCFCTB/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":"2026-07-17T17:31:52Z","links":{"resolver":"https://pith.science/pith/O3AY3JOTSKKRLLPFWXP2GCFCTB","bundle":"https://pith.science/pith/O3AY3JOTSKKRLLPFWXP2GCFCTB/bundle.json","state":"https://pith.science/pith/O3AY3JOTSKKRLLPFWXP2GCFCTB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O3AY3JOTSKKRLLPFWXP2GCFCTB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:O3AY3JOTSKKRLLPFWXP2GCFCTB","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":"6ef567eed86b08e98487441ab7aed8c2eabb19feba02093fe6cd745615818bc0","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-11-21T11:48:07Z","title_canon_sha256":"60cd1769d21dad267a90c6a85fe576a4449ef6f0684ceac137774ef2589b04d3"},"schema_version":"1.0","source":{"id":"2011.10778","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.10778","created_at":"2026-07-05T01:56:16Z"},{"alias_kind":"arxiv_version","alias_value":"2011.10778v1","created_at":"2026-07-05T01:56:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.10778","created_at":"2026-07-05T01:56:16Z"},{"alias_kind":"pith_short_12","alias_value":"O3AY3JOTSKKR","created_at":"2026-07-05T01:56:16Z"},{"alias_kind":"pith_short_16","alias_value":"O3AY3JOTSKKRLLPF","created_at":"2026-07-05T01:56:16Z"},{"alias_kind":"pith_short_8","alias_value":"O3AY3JOT","created_at":"2026-07-05T01:56:16Z"}],"graph_snapshots":[{"event_id":"sha256:0996dea37c2a7a7d85b4f1dd2d371f1b807141a8e926c79ba95a9d631237f950","target":"graph","created_at":"2026-07-05T01:56:16Z","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/2011.10778/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate several important issues regarding the Random Batch Method (RBM) for second order interacting particle systems. We first show the uniform-in-time strong convergence for second order systems under suitable contraction conditions. Secondly, we propose the application of RBM for singular interaction kernels via kernel splitting strategy, and investigate numerically the application to molecular dynamics.","authors_text":"Lei Li, Shi Jin, Yiqun Sun","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-11-21T11:48:07Z","title":"On the Random Batch Method for second order interacting particle systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.10778","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:c0b64713b02b6e8386ed8db4ffb54c8ced2dc9e967d714d78f9ac4c1283371b9","target":"record","created_at":"2026-07-05T01:56:16Z","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":"6ef567eed86b08e98487441ab7aed8c2eabb19feba02093fe6cd745615818bc0","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-11-21T11:48:07Z","title_canon_sha256":"60cd1769d21dad267a90c6a85fe576a4449ef6f0684ceac137774ef2589b04d3"},"schema_version":"1.0","source":{"id":"2011.10778","kind":"arxiv","version":1}},"canonical_sha256":"76c18da5d3929515ade5b5dfa308a2987bfeb08287ba690188393b53ce559446","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76c18da5d3929515ade5b5dfa308a2987bfeb08287ba690188393b53ce559446","first_computed_at":"2026-07-05T01:56:16.097673Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:56:16.097673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q2O9bAqvjgcjlBIpIwFLCZVgi/OC6IE4KyD9C1k5pNHT4fHDYnoQlVwmewOGIXGXxj8Fy0F4/nEnDnzsQnOzDA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:56:16.098092Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.10778","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0b64713b02b6e8386ed8db4ffb54c8ced2dc9e967d714d78f9ac4c1283371b9","sha256:0996dea37c2a7a7d85b4f1dd2d371f1b807141a8e926c79ba95a9d631237f950"],"state_sha256":"476506466447f29958ab1f0e53f510e6d617ef5566b6e94f68fd6906e5f999f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iQv1TCIqr2x/7R9jbwweOlVoda/estvJHzU9NUISmD2vgyFYxIs6A1eb5OLFVZthg7nIqEbgrY5e4LX37KlSDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-17T17:31:52.188146Z","bundle_sha256":"bd5870ea5a8c7551a7491e8429fc1017a6787501294febdff386ae2ddc844fc8"}}