{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:J6AXHK5D6ZCIM5RMEHVA33N5JJ","short_pith_number":"pith:J6AXHK5D","canonical_record":{"source":{"id":"1410.7617","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NA","submitted_at":"2014-10-28T13:38:50Z","cross_cats_sorted":[],"title_canon_sha256":"6aeee64820382ae66294df537fe0dc645c1cc9c2be47673207751014dfbfc45a","abstract_canon_sha256":"30e2b5ece39c34c8b0f60fe39ee17af40629763244eed14b963daf1fb10ede9f"},"schema_version":"1.0"},"canonical_sha256":"4f8173aba3f64486762c21ea0dedbd4a553b70c1e11ec714eced76a08fa70379","source":{"kind":"arxiv","id":"1410.7617","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7617","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7617v1","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7617","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"pith_short_12","alias_value":"J6AXHK5D6ZCI","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"J6AXHK5D6ZCIM5RM","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"J6AXHK5D","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:J6AXHK5D6ZCIM5RMEHVA33N5JJ","target":"record","payload":{"canonical_record":{"source":{"id":"1410.7617","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NA","submitted_at":"2014-10-28T13:38:50Z","cross_cats_sorted":[],"title_canon_sha256":"6aeee64820382ae66294df537fe0dc645c1cc9c2be47673207751014dfbfc45a","abstract_canon_sha256":"30e2b5ece39c34c8b0f60fe39ee17af40629763244eed14b963daf1fb10ede9f"},"schema_version":"1.0"},"canonical_sha256":"4f8173aba3f64486762c21ea0dedbd4a553b70c1e11ec714eced76a08fa70379","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:09.874738Z","signature_b64":"yEfFJ+jql/Pes8scYm1A0ts+Gw8L7JwN7xDeH2tRsSefrkpGy7uGKwj+bWOUPlk8dCIf+HWDwNcOYMqnefWMCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f8173aba3f64486762c21ea0dedbd4a553b70c1e11ec714eced76a08fa70379","last_reissued_at":"2026-05-18T02:39:09.874061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:09.874061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.7617","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":"2026-05-18T02:39:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"peIlAUdZtSDVOc7MO4IW2ocn+JM3f0jmHl3wXd+6cdcJeV5lyNZuxHLdM7uhwPIm3xHjLuSkmdbCa9mffCMlAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T05:46:09.987762Z"},"content_sha256":"03774e9d6fc207691e98063fe9a7bc5580d959b64e3d26e07e4ec7fffd8477b6","schema_version":"1.0","event_id":"sha256:03774e9d6fc207691e98063fe9a7bc5580d959b64e3d26e07e4ec7fffd8477b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:J6AXHK5D6ZCIM5RMEHVA33N5JJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Exact Rescaling Velocity Method for some Kinetic Flocking Models","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Changhui Tan, Thomas Rey","submitted_at":"2014-10-28T13:38:50Z","abstract_excerpt":"In this work, we discuss kinetic descriptions of flocking models, of the so-called Cucker-Smale and Motsch-Tadmor types. These models are given by Vlasov-type equations where the interactions taken into account are only given long-range bi-particles interaction potential. We introduce a new exact rescaling velocity method, inspired by a recent work of Filbet and Rey, allowing to observe numerically the flocking behavior of the solutions to these equations, without a need of remeshing or taking a very fine grid in the velocity space. To stabilize the exact method, we also introduce a modificati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7617","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":""},"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":"2026-05-18T02:39:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MVwQ4pdiIGGHkGqsFtvMM+Al4/TCayKL5m/bGb7kGgoOTFEy0Rz78DkDhHY/M3Pn+qcM3UvcRKcXhByH4iU1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T05:46:09.988100Z"},"content_sha256":"c727ab87499393cb9995e7c66812a5f304d5cbf03b0e1b307a6149a4d8eb9499","schema_version":"1.0","event_id":"sha256:c727ab87499393cb9995e7c66812a5f304d5cbf03b0e1b307a6149a4d8eb9499"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J6AXHK5D6ZCIM5RMEHVA33N5JJ/bundle.json","state_url":"https://pith.science/pith/J6AXHK5D6ZCIM5RMEHVA33N5JJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J6AXHK5D6ZCIM5RMEHVA33N5JJ/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":"2026-06-27T05:46:09Z","links":{"resolver":"https://pith.science/pith/J6AXHK5D6ZCIM5RMEHVA33N5JJ","bundle":"https://pith.science/pith/J6AXHK5D6ZCIM5RMEHVA33N5JJ/bundle.json","state":"https://pith.science/pith/J6AXHK5D6ZCIM5RMEHVA33N5JJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J6AXHK5D6ZCIM5RMEHVA33N5JJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:J6AXHK5D6ZCIM5RMEHVA33N5JJ","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":"30e2b5ece39c34c8b0f60fe39ee17af40629763244eed14b963daf1fb10ede9f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NA","submitted_at":"2014-10-28T13:38:50Z","title_canon_sha256":"6aeee64820382ae66294df537fe0dc645c1cc9c2be47673207751014dfbfc45a"},"schema_version":"1.0","source":{"id":"1410.7617","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7617","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7617v1","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7617","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"pith_short_12","alias_value":"J6AXHK5D6ZCI","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"J6AXHK5D6ZCIM5RM","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"J6AXHK5D","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:c727ab87499393cb9995e7c66812a5f304d5cbf03b0e1b307a6149a4d8eb9499","target":"graph","created_at":"2026-05-18T02:39:09Z","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"},"paper":{"abstract_excerpt":"In this work, we discuss kinetic descriptions of flocking models, of the so-called Cucker-Smale and Motsch-Tadmor types. These models are given by Vlasov-type equations where the interactions taken into account are only given long-range bi-particles interaction potential. We introduce a new exact rescaling velocity method, inspired by a recent work of Filbet and Rey, allowing to observe numerically the flocking behavior of the solutions to these equations, without a need of remeshing or taking a very fine grid in the velocity space. To stabilize the exact method, we also introduce a modificati","authors_text":"Changhui Tan, Thomas Rey","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NA","submitted_at":"2014-10-28T13:38:50Z","title":"An Exact Rescaling Velocity Method for some Kinetic Flocking Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7617","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":"sha256:03774e9d6fc207691e98063fe9a7bc5580d959b64e3d26e07e4ec7fffd8477b6","target":"record","created_at":"2026-05-18T02:39:09Z","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":"30e2b5ece39c34c8b0f60fe39ee17af40629763244eed14b963daf1fb10ede9f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NA","submitted_at":"2014-10-28T13:38:50Z","title_canon_sha256":"6aeee64820382ae66294df537fe0dc645c1cc9c2be47673207751014dfbfc45a"},"schema_version":"1.0","source":{"id":"1410.7617","kind":"arxiv","version":1}},"canonical_sha256":"4f8173aba3f64486762c21ea0dedbd4a553b70c1e11ec714eced76a08fa70379","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f8173aba3f64486762c21ea0dedbd4a553b70c1e11ec714eced76a08fa70379","first_computed_at":"2026-05-18T02:39:09.874061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:09.874061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yEfFJ+jql/Pes8scYm1A0ts+Gw8L7JwN7xDeH2tRsSefrkpGy7uGKwj+bWOUPlk8dCIf+HWDwNcOYMqnefWMCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:09.874738Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.7617","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03774e9d6fc207691e98063fe9a7bc5580d959b64e3d26e07e4ec7fffd8477b6","sha256:c727ab87499393cb9995e7c66812a5f304d5cbf03b0e1b307a6149a4d8eb9499"],"state_sha256":"137adb9a967e182632e196f4186e241b075cda603b93632f5fec1dbd77537c39"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iUQeFfGzFmd+81QJyWxrJQmskMbVUSN/6JzZ/uYqqSu+Xm632W/afWpiRleUroAC2EFSzq2ZTP2WzuylTgNLAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T05:46:09.989986Z","bundle_sha256":"1d1687d1be0357d23d340e8299f5905a0e942da32da33330876599aa218e8593"}}