{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Z6Y4HO65PJRJ5YDLOVFXKWX6OW","short_pith_number":"pith:Z6Y4HO65","canonical_record":{"source":{"id":"1102.5575","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-28T02:34:10Z","cross_cats_sorted":[],"title_canon_sha256":"85499cc6cf50c43ca4c11cdd5631039a2127a53479d9dab8dcd50698a40fd528","abstract_canon_sha256":"6b274322c91aaabef7928d084da757dd70ee249bb9bf3f4cbaa80cfa6507e8cb"},"schema_version":"1.0"},"canonical_sha256":"cfb1c3bbdd7a629ee06b754b755afe758a18161f6e4a6ec1ae9f4135c286e385","source":{"kind":"arxiv","id":"1102.5575","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.5575","created_at":"2026-05-18T02:03:04Z"},{"alias_kind":"arxiv_version","alias_value":"1102.5575v2","created_at":"2026-05-18T02:03:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5575","created_at":"2026-05-18T02:03:04Z"},{"alias_kind":"pith_short_12","alias_value":"Z6Y4HO65PJRJ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z6Y4HO65PJRJ5YDL","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z6Y4HO65","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Z6Y4HO65PJRJ5YDLOVFXKWX6OW","target":"record","payload":{"canonical_record":{"source":{"id":"1102.5575","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-28T02:34:10Z","cross_cats_sorted":[],"title_canon_sha256":"85499cc6cf50c43ca4c11cdd5631039a2127a53479d9dab8dcd50698a40fd528","abstract_canon_sha256":"6b274322c91aaabef7928d084da757dd70ee249bb9bf3f4cbaa80cfa6507e8cb"},"schema_version":"1.0"},"canonical_sha256":"cfb1c3bbdd7a629ee06b754b755afe758a18161f6e4a6ec1ae9f4135c286e385","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:04.142037Z","signature_b64":"PnlHg2OIkUWckKR7Q4zbPlxgyAOLbTwYOzFjCm14xxpC2ODCwhNlYNZO/CRND1wMKl0XtryQMR5CeVacJwpDAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfb1c3bbdd7a629ee06b754b755afe758a18161f6e4a6ec1ae9f4135c286e385","last_reissued_at":"2026-05-18T02:03:04.141473Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:04.141473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.5575","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:03:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t18QX/ybQGrZCdNh71zCmMFZZT6bnYtzSz7EG3R5KNufj2buIr78PcidDyjla4lyNNOKW5gR3EAtNESKnobDAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:21:42.110421Z"},"content_sha256":"c08dc4a15c45799641478c397d67c0d61ffbb0278f4f05a1c3b3bf02bbdd9a35","schema_version":"1.0","event_id":"sha256:c08dc4a15c45799641478c397d67c0d61ffbb0278f4f05a1c3b3bf02bbdd9a35"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Z6Y4HO65PJRJ5YDLOVFXKWX6OW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new model for self-organized dynamics and its flocking behavior","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eitan Tadmor, Sebastien Motsch","submitted_at":"2011-02-28T02:34:10Z","abstract_excerpt":"We introduce a model for self-organized dynamics which, we argue, addresses several drawbacks of the celebrated Cucker-Smale (C-S) model. The proposed model does not only take into account the distance between agents, but instead, the influence between agents is scaled in term of their relative distance. Consequently, our model does not involve any explicit dependence on the number of agents; only their geometry in phase space is taken into account. The use of relative distances destroys the symmetry property of the original C-S model, which was the key for the various recent studies of C-S fl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5575","kind":"arxiv","version":2},"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":"2026-05-18T02:03:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SSl4rM2RfX8ldPXbodLoKbDDxnUvHds88jxtNLxR91gXo7r/v8xbLh6OslzBA8m4Qx5EzgvpBA+9K68CdGEaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:21:42.111042Z"},"content_sha256":"33648b3d07ca5580c3fd2ff949624e17a2018cb303e24f0819907bc7d73513c5","schema_version":"1.0","event_id":"sha256:33648b3d07ca5580c3fd2ff949624e17a2018cb303e24f0819907bc7d73513c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z6Y4HO65PJRJ5YDLOVFXKWX6OW/bundle.json","state_url":"https://pith.science/pith/Z6Y4HO65PJRJ5YDLOVFXKWX6OW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z6Y4HO65PJRJ5YDLOVFXKWX6OW/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":"2026-06-06T19:21:42Z","links":{"resolver":"https://pith.science/pith/Z6Y4HO65PJRJ5YDLOVFXKWX6OW","bundle":"https://pith.science/pith/Z6Y4HO65PJRJ5YDLOVFXKWX6OW/bundle.json","state":"https://pith.science/pith/Z6Y4HO65PJRJ5YDLOVFXKWX6OW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z6Y4HO65PJRJ5YDLOVFXKWX6OW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Z6Y4HO65PJRJ5YDLOVFXKWX6OW","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":"6b274322c91aaabef7928d084da757dd70ee249bb9bf3f4cbaa80cfa6507e8cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-28T02:34:10Z","title_canon_sha256":"85499cc6cf50c43ca4c11cdd5631039a2127a53479d9dab8dcd50698a40fd528"},"schema_version":"1.0","source":{"id":"1102.5575","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.5575","created_at":"2026-05-18T02:03:04Z"},{"alias_kind":"arxiv_version","alias_value":"1102.5575v2","created_at":"2026-05-18T02:03:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5575","created_at":"2026-05-18T02:03:04Z"},{"alias_kind":"pith_short_12","alias_value":"Z6Y4HO65PJRJ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z6Y4HO65PJRJ5YDL","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z6Y4HO65","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:33648b3d07ca5580c3fd2ff949624e17a2018cb303e24f0819907bc7d73513c5","target":"graph","created_at":"2026-05-18T02:03:04Z","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":"We introduce a model for self-organized dynamics which, we argue, addresses several drawbacks of the celebrated Cucker-Smale (C-S) model. The proposed model does not only take into account the distance between agents, but instead, the influence between agents is scaled in term of their relative distance. Consequently, our model does not involve any explicit dependence on the number of agents; only their geometry in phase space is taken into account. The use of relative distances destroys the symmetry property of the original C-S model, which was the key for the various recent studies of C-S fl","authors_text":"Eitan Tadmor, Sebastien Motsch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-28T02:34:10Z","title":"A new model for self-organized dynamics and its flocking behavior"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5575","kind":"arxiv","version":2},"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:c08dc4a15c45799641478c397d67c0d61ffbb0278f4f05a1c3b3bf02bbdd9a35","target":"record","created_at":"2026-05-18T02:03:04Z","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":"6b274322c91aaabef7928d084da757dd70ee249bb9bf3f4cbaa80cfa6507e8cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-28T02:34:10Z","title_canon_sha256":"85499cc6cf50c43ca4c11cdd5631039a2127a53479d9dab8dcd50698a40fd528"},"schema_version":"1.0","source":{"id":"1102.5575","kind":"arxiv","version":2}},"canonical_sha256":"cfb1c3bbdd7a629ee06b754b755afe758a18161f6e4a6ec1ae9f4135c286e385","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfb1c3bbdd7a629ee06b754b755afe758a18161f6e4a6ec1ae9f4135c286e385","first_computed_at":"2026-05-18T02:03:04.141473Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:04.141473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PnlHg2OIkUWckKR7Q4zbPlxgyAOLbTwYOzFjCm14xxpC2ODCwhNlYNZO/CRND1wMKl0XtryQMR5CeVacJwpDAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:04.142037Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.5575","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c08dc4a15c45799641478c397d67c0d61ffbb0278f4f05a1c3b3bf02bbdd9a35","sha256:33648b3d07ca5580c3fd2ff949624e17a2018cb303e24f0819907bc7d73513c5"],"state_sha256":"66c763f0cded02681fc3d6debdc67d5ace18066430be72f3dccd9cf820dad4a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"80MMgthquP2IFIg7iPvY6CbJoFtJlkrUVRVairTrJvZkrK1x8/17kQ4IYDP4LurpHkJj50RUkPg7jhSWeDZSAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:21:42.114304Z","bundle_sha256":"61a555c84f7a2c3b6c53eec3b4a5331fd9c113bf7e0544545d1ab232b81025fc"}}