{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:763ABJAJEIEE6Z6FCBPAX2ABDH","short_pith_number":"pith:763ABJAJ","canonical_record":{"source":{"id":"2311.00902","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2023-11-01T23:45:15Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA","math.ST","stat.TH"],"title_canon_sha256":"a8231c648024dd72085e4e84d19e2dd946c3c2a58b1d2f986a8c199981617c27","abstract_canon_sha256":"79f0b20d3dfac854c86cda7db6a60190587bfb5c3e99a261e22076029e3f02cb"},"schema_version":"1.0"},"canonical_sha256":"ffb600a40922084f67c5105e0be80119dd984ec1a21c5ea4269f7dd242816ad8","source":{"kind":"arxiv","id":"2311.00902","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.00902","created_at":"2026-07-05T07:08:17Z"},{"alias_kind":"arxiv_version","alias_value":"2311.00902v1","created_at":"2026-07-05T07:08:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.00902","created_at":"2026-07-05T07:08:17Z"},{"alias_kind":"pith_short_12","alias_value":"763ABJAJEIEE","created_at":"2026-07-05T07:08:17Z"},{"alias_kind":"pith_short_16","alias_value":"763ABJAJEIEE6Z6F","created_at":"2026-07-05T07:08:17Z"},{"alias_kind":"pith_short_8","alias_value":"763ABJAJ","created_at":"2026-07-05T07:08:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:763ABJAJEIEE6Z6FCBPAX2ABDH","target":"record","payload":{"canonical_record":{"source":{"id":"2311.00902","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2023-11-01T23:45:15Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA","math.ST","stat.TH"],"title_canon_sha256":"a8231c648024dd72085e4e84d19e2dd946c3c2a58b1d2f986a8c199981617c27","abstract_canon_sha256":"79f0b20d3dfac854c86cda7db6a60190587bfb5c3e99a261e22076029e3f02cb"},"schema_version":"1.0"},"canonical_sha256":"ffb600a40922084f67c5105e0be80119dd984ec1a21c5ea4269f7dd242816ad8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:08:17.266895Z","signature_b64":"1ZpNuof+am040ha7bMq59EMASvo+a84fbU4okowideRHvWCGSGWNMqohRbDaa7780GCV2dV1dgkzpFbIaYOCCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffb600a40922084f67c5105e0be80119dd984ec1a21c5ea4269f7dd242816ad8","last_reissued_at":"2026-07-05T07:08:17.266426Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:08:17.266426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.00902","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":"2026-07-05T07:08:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QBSkbDrW30fbcGm9BPI1nDkYPfn/lwnWrFHD9xdfVc9fXbMxsr5V2btyKzVsCXr5fcn2q3zvK3l8+s2TwIdxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:04:41.802131Z"},"content_sha256":"4a2e29ce0aff8917d9da5b7a21355fc2402b9aa7e952dd8804f1e9ac6c69aa5e","schema_version":"1.0","event_id":"sha256:4a2e29ce0aff8917d9da5b7a21355fc2402b9aa7e952dd8804f1e9ac6c69aa5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:763ABJAJEIEE6Z6FCBPAX2ABDH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Data-Driven Model Selections of Second-Order Particle Dynamics via Integrating Gaussian Processes with Low-Dimensional Interacting Structures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Charles Kulick, Jinchao Feng, Sui Tang","submitted_at":"2023-11-01T23:45:15Z","abstract_excerpt":"In this paper, we focus on the data-driven discovery of a general second-order particle-based model that contains many state-of-the-art models for modeling the aggregation and collective behavior of interacting agents of similar size and body type. This model takes the form of a high-dimensional system of ordinary differential equations parameterized by two interaction kernels that appraise the alignment of positions and velocities. We propose a Gaussian Process-based approach to this problem, where the unknown model parameters are marginalized by using two independent Gaussian Process (GP) pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.00902","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/2311.00902/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":"2026-07-05T07:08:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"57GoPQhdZWpXrwIjRSpDDTyIK7RY3XbDAZM/59GQ2RDb/e5wxZ+qD1Q8kvk2dhy1BkxHikm+3zAgnz083jxPBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:04:41.802693Z"},"content_sha256":"3b4bc8022af5dea863589fd7953ae417a26ff3bf776b59473a27516229c57e3e","schema_version":"1.0","event_id":"sha256:3b4bc8022af5dea863589fd7953ae417a26ff3bf776b59473a27516229c57e3e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/763ABJAJEIEE6Z6FCBPAX2ABDH/bundle.json","state_url":"https://pith.science/pith/763ABJAJEIEE6Z6FCBPAX2ABDH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/763ABJAJEIEE6Z6FCBPAX2ABDH/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":"2026-07-07T13:04:41Z","links":{"resolver":"https://pith.science/pith/763ABJAJEIEE6Z6FCBPAX2ABDH","bundle":"https://pith.science/pith/763ABJAJEIEE6Z6FCBPAX2ABDH/bundle.json","state":"https://pith.science/pith/763ABJAJEIEE6Z6FCBPAX2ABDH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/763ABJAJEIEE6Z6FCBPAX2ABDH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:763ABJAJEIEE6Z6FCBPAX2ABDH","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":"79f0b20d3dfac854c86cda7db6a60190587bfb5c3e99a261e22076029e3f02cb","cross_cats_sorted":["cs.LG","cs.NA","math.NA","math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2023-11-01T23:45:15Z","title_canon_sha256":"a8231c648024dd72085e4e84d19e2dd946c3c2a58b1d2f986a8c199981617c27"},"schema_version":"1.0","source":{"id":"2311.00902","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.00902","created_at":"2026-07-05T07:08:17Z"},{"alias_kind":"arxiv_version","alias_value":"2311.00902v1","created_at":"2026-07-05T07:08:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.00902","created_at":"2026-07-05T07:08:17Z"},{"alias_kind":"pith_short_12","alias_value":"763ABJAJEIEE","created_at":"2026-07-05T07:08:17Z"},{"alias_kind":"pith_short_16","alias_value":"763ABJAJEIEE6Z6F","created_at":"2026-07-05T07:08:17Z"},{"alias_kind":"pith_short_8","alias_value":"763ABJAJ","created_at":"2026-07-05T07:08:17Z"}],"graph_snapshots":[{"event_id":"sha256:3b4bc8022af5dea863589fd7953ae417a26ff3bf776b59473a27516229c57e3e","target":"graph","created_at":"2026-07-05T07:08:17Z","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/2311.00902/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we focus on the data-driven discovery of a general second-order particle-based model that contains many state-of-the-art models for modeling the aggregation and collective behavior of interacting agents of similar size and body type. This model takes the form of a high-dimensional system of ordinary differential equations parameterized by two interaction kernels that appraise the alignment of positions and velocities. We propose a Gaussian Process-based approach to this problem, where the unknown model parameters are marginalized by using two independent Gaussian Process (GP) pr","authors_text":"Charles Kulick, Jinchao Feng, Sui Tang","cross_cats":["cs.LG","cs.NA","math.NA","math.ST","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2023-11-01T23:45:15Z","title":"Data-Driven Model Selections of Second-Order Particle Dynamics via Integrating Gaussian Processes with Low-Dimensional Interacting Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.00902","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":"sha256:4a2e29ce0aff8917d9da5b7a21355fc2402b9aa7e952dd8804f1e9ac6c69aa5e","target":"record","created_at":"2026-07-05T07:08:17Z","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":"79f0b20d3dfac854c86cda7db6a60190587bfb5c3e99a261e22076029e3f02cb","cross_cats_sorted":["cs.LG","cs.NA","math.NA","math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2023-11-01T23:45:15Z","title_canon_sha256":"a8231c648024dd72085e4e84d19e2dd946c3c2a58b1d2f986a8c199981617c27"},"schema_version":"1.0","source":{"id":"2311.00902","kind":"arxiv","version":1}},"canonical_sha256":"ffb600a40922084f67c5105e0be80119dd984ec1a21c5ea4269f7dd242816ad8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffb600a40922084f67c5105e0be80119dd984ec1a21c5ea4269f7dd242816ad8","first_computed_at":"2026-07-05T07:08:17.266426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:08:17.266426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1ZpNuof+am040ha7bMq59EMASvo+a84fbU4okowideRHvWCGSGWNMqohRbDaa7780GCV2dV1dgkzpFbIaYOCCg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:08:17.266895Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.00902","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a2e29ce0aff8917d9da5b7a21355fc2402b9aa7e952dd8804f1e9ac6c69aa5e","sha256:3b4bc8022af5dea863589fd7953ae417a26ff3bf776b59473a27516229c57e3e"],"state_sha256":"949e38d61c9b14b97be5466a2caa7932acd57a37d61889ee0ecec11b8b480295"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LtalVQQ0IBBBAQPTEwe+/zgnfoADr98BoE9v3mRSUHbvdsPnCQnr3G9yfJae0v3zNNHpyipE/KX9yebqr9XWDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T13:04:41.805239Z","bundle_sha256":"c738754a5fb9903c95e63708d9872174f92eed084119a8f9b3c6eef1c3ca1307"}}