{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5NXDSEE7FRB5CXZVHMOVCTH5TQ","short_pith_number":"pith:5NXDSEE7","canonical_record":{"source":{"id":"1507.02980","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-07T10:41:37Z","cross_cats_sorted":["cs.SY","eess.SY","math.DS","math.OC","q-bio.CB"],"title_canon_sha256":"cb607d231e46fee9dfe6ef284ebcd45988616a974841b5460b7a2ca5894b3739","abstract_canon_sha256":"751c7609fb7c0d2abee472d2722854171e24d8d3da4468a9811199793f5fad76"},"schema_version":"1.0"},"canonical_sha256":"eb6e39109f2c43d15f353b1d514cfd9c395f110bf762eda0ec288e99d1b0da5f","source":{"kind":"arxiv","id":"1507.02980","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02980","created_at":"2026-06-04T17:09:23Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02980v2","created_at":"2026-06-04T17:09:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02980","created_at":"2026-06-04T17:09:23Z"},{"alias_kind":"pith_short_12","alias_value":"5NXDSEE7FRB5","created_at":"2026-06-04T17:09:23Z"},{"alias_kind":"pith_short_16","alias_value":"5NXDSEE7FRB5CXZV","created_at":"2026-06-04T17:09:23Z"},{"alias_kind":"pith_short_8","alias_value":"5NXDSEE7","created_at":"2026-06-04T17:09:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5NXDSEE7FRB5CXZVHMOVCTH5TQ","target":"record","payload":{"canonical_record":{"source":{"id":"1507.02980","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-07T10:41:37Z","cross_cats_sorted":["cs.SY","eess.SY","math.DS","math.OC","q-bio.CB"],"title_canon_sha256":"cb607d231e46fee9dfe6ef284ebcd45988616a974841b5460b7a2ca5894b3739","abstract_canon_sha256":"751c7609fb7c0d2abee472d2722854171e24d8d3da4468a9811199793f5fad76"},"schema_version":"1.0"},"canonical_sha256":"eb6e39109f2c43d15f353b1d514cfd9c395f110bf762eda0ec288e99d1b0da5f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T17:09:23.732476Z","signature_b64":"TMle+3mPVONT2JjbPM57gpgUBc3C8bmyKpk2b4fykkJBOcEKPIw61hbunKh3diPLVAetssqU8ojqV6lFcgStAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb6e39109f2c43d15f353b1d514cfd9c395f110bf762eda0ec288e99d1b0da5f","last_reissued_at":"2026-06-04T17:09:23.731951Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T17:09:23.731951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.02980","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":"2026-06-04T17:09:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+tQ4XCoWd/ZLBvvcNnrjS9G+SAQbFGVNFSxdKvgPynBtWzCOZY3mNVGkoSbTv01QGycr7ZxdVgqNPEPXnHRoBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:16:39.542766Z"},"content_sha256":"bb1b95fd0b5a7934d6d078e79a58bc5d6c242b40287491175e9b8d490694a440","schema_version":"1.0","event_id":"sha256:bb1b95fd0b5a7934d6d078e79a58bc5d6c242b40287491175e9b8d490694a440"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5NXDSEE7FRB5CXZVHMOVCTH5TQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A hybrid mathematical model of collective motion under alignment and chemotaxis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","eess.SY","math.DS","math.OC","q-bio.CB"],"primary_cat":"math.CA","authors_text":"Antonia Vecchio, Eleonora Messina, Ezio Di Costanzo, Marta Menci, Roberto Natalini","submitted_at":"2015-07-07T10:41:37Z","abstract_excerpt":"In this paper we propose and study a hybrid discrete in continuous mathematical model of collective motion under alignment and chemotaxis effect. Starting from the paper by Di Costanzo et al (2015a), in which the Cucker-Smale model (Cucker and Smale, 2007) was coupled with other cell mechanisms, to describe the cell migration and self-organization in the zebrafish lateral line primordium, we introduce a simplified model in which the coupling between an alignment and chemotaxis mechanism acts on a system of interacting particles. In particular we rely on a hybrid description in which the agents"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02980","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1507.02980/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":"2026-06-04T17:09:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W9RbRxl7ZjCc1lRvM5VTj7sGYGpcVOtMyTE38HNvPyhP+/cFtFRwvaVBbaIKrGSXXI5TYpX96dStgHgP85uXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:16:39.543146Z"},"content_sha256":"b000e2ff8c1cdebe88ab1737cf3aa6bdd1aadc96beb2f8089fedd69db5a50751","schema_version":"1.0","event_id":"sha256:b000e2ff8c1cdebe88ab1737cf3aa6bdd1aadc96beb2f8089fedd69db5a50751"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5NXDSEE7FRB5CXZVHMOVCTH5TQ/bundle.json","state_url":"https://pith.science/pith/5NXDSEE7FRB5CXZVHMOVCTH5TQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5NXDSEE7FRB5CXZVHMOVCTH5TQ/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":"2026-06-12T08:16:39Z","links":{"resolver":"https://pith.science/pith/5NXDSEE7FRB5CXZVHMOVCTH5TQ","bundle":"https://pith.science/pith/5NXDSEE7FRB5CXZVHMOVCTH5TQ/bundle.json","state":"https://pith.science/pith/5NXDSEE7FRB5CXZVHMOVCTH5TQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5NXDSEE7FRB5CXZVHMOVCTH5TQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5NXDSEE7FRB5CXZVHMOVCTH5TQ","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":"751c7609fb7c0d2abee472d2722854171e24d8d3da4468a9811199793f5fad76","cross_cats_sorted":["cs.SY","eess.SY","math.DS","math.OC","q-bio.CB"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-07T10:41:37Z","title_canon_sha256":"cb607d231e46fee9dfe6ef284ebcd45988616a974841b5460b7a2ca5894b3739"},"schema_version":"1.0","source":{"id":"1507.02980","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02980","created_at":"2026-06-04T17:09:23Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02980v2","created_at":"2026-06-04T17:09:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02980","created_at":"2026-06-04T17:09:23Z"},{"alias_kind":"pith_short_12","alias_value":"5NXDSEE7FRB5","created_at":"2026-06-04T17:09:23Z"},{"alias_kind":"pith_short_16","alias_value":"5NXDSEE7FRB5CXZV","created_at":"2026-06-04T17:09:23Z"},{"alias_kind":"pith_short_8","alias_value":"5NXDSEE7","created_at":"2026-06-04T17:09:23Z"}],"graph_snapshots":[{"event_id":"sha256:b000e2ff8c1cdebe88ab1737cf3aa6bdd1aadc96beb2f8089fedd69db5a50751","target":"graph","created_at":"2026-06-04T17:09:23Z","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/1507.02980/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we propose and study a hybrid discrete in continuous mathematical model of collective motion under alignment and chemotaxis effect. Starting from the paper by Di Costanzo et al (2015a), in which the Cucker-Smale model (Cucker and Smale, 2007) was coupled with other cell mechanisms, to describe the cell migration and self-organization in the zebrafish lateral line primordium, we introduce a simplified model in which the coupling between an alignment and chemotaxis mechanism acts on a system of interacting particles. In particular we rely on a hybrid description in which the agents","authors_text":"Antonia Vecchio, Eleonora Messina, Ezio Di Costanzo, Marta Menci, Roberto Natalini","cross_cats":["cs.SY","eess.SY","math.DS","math.OC","q-bio.CB"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-07T10:41:37Z","title":"A hybrid mathematical model of collective motion under alignment and chemotaxis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02980","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:bb1b95fd0b5a7934d6d078e79a58bc5d6c242b40287491175e9b8d490694a440","target":"record","created_at":"2026-06-04T17:09:23Z","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":"751c7609fb7c0d2abee472d2722854171e24d8d3da4468a9811199793f5fad76","cross_cats_sorted":["cs.SY","eess.SY","math.DS","math.OC","q-bio.CB"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-07-07T10:41:37Z","title_canon_sha256":"cb607d231e46fee9dfe6ef284ebcd45988616a974841b5460b7a2ca5894b3739"},"schema_version":"1.0","source":{"id":"1507.02980","kind":"arxiv","version":2}},"canonical_sha256":"eb6e39109f2c43d15f353b1d514cfd9c395f110bf762eda0ec288e99d1b0da5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb6e39109f2c43d15f353b1d514cfd9c395f110bf762eda0ec288e99d1b0da5f","first_computed_at":"2026-06-04T17:09:23.731951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T17:09:23.731951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TMle+3mPVONT2JjbPM57gpgUBc3C8bmyKpk2b4fykkJBOcEKPIw61hbunKh3diPLVAetssqU8ojqV6lFcgStAA==","signature_status":"signed_v1","signed_at":"2026-06-04T17:09:23.732476Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02980","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb1b95fd0b5a7934d6d078e79a58bc5d6c242b40287491175e9b8d490694a440","sha256:b000e2ff8c1cdebe88ab1737cf3aa6bdd1aadc96beb2f8089fedd69db5a50751"],"state_sha256":"fadfc4745aa353896f2067a39baed24708b2dd10323e481918eb039ef6768d07"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XN6MeA1pjTW99f6WWl2SN+HP1ADDvGdrpln3ccHESLedInucCqwq0D8MNKGWjYqUiXteiNOZgeLisLVwy0HLBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T08:16:39.545214Z","bundle_sha256":"92d792b2cb234fdeffeb2d4f6f366f864fa982dd3d06ae0287e7157097ba1502"}}