{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:KSAZQWCL3QLPDIST4VVP6VM7PC","short_pith_number":"pith:KSAZQWCL","schema_version":"1.0","canonical_sha256":"548198584bdc16f1a253e56aff559f7888b7b93b5e17a5d887314c86c3afb252","source":{"kind":"arxiv","id":"1609.03447","version":1},"attestation_state":"computed","paper":{"title":"Sharp conditions to avoid collisions in singular Cucker-Smale interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jan Peszek, Jose A. Carrillo, Piotr B. Mucha, Young-Pil Choi","submitted_at":"2016-09-12T15:26:05Z","abstract_excerpt":"We consider the Cucker-Smale flocking model with a singular communication weight $\\psi(s) = s^{-\\alpha}$ with $\\alpha > 0$. We provide a critical value of the exponent $\\alpha$ in the communication weight leading to global regularity of solutions or finite-time collision between particles. For $\\alpha \\geq 1$, we show that there is no collision between particles in finite time if they are placed in different positions initially. For $\\alpha\\geq 2$ we investigate a version of the Cucker-Smale model with expanded singularity i.e. with weight $\\psi_\\delta(s) = (s-\\delta)^{-\\alpha}$, $\\delta\\geq 0"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1609.03447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-12T15:26:05Z","cross_cats_sorted":[],"title_canon_sha256":"e6cc9c8a31763a20b4bd7ecbc301c1a5a896f9c5898dd1280c687bd61fe64547","abstract_canon_sha256":"6f83af68cf832c7a9312b7f94d695339bdab06f40828e8ea9827faa9ef2c2451"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:46.932293Z","signature_b64":"sXPNiwm6Rh7FtihpIV/T0JYFYKB4wUcCMRDBH0Y5wOophd5SO1cwhA/T5HylbdIGii8Ie2OYwZJYJ6N63h9XBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"548198584bdc16f1a253e56aff559f7888b7b93b5e17a5d887314c86c3afb252","last_reissued_at":"2026-05-18T01:04:46.931632Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:46.931632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp conditions to avoid collisions in singular Cucker-Smale interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jan Peszek, Jose A. Carrillo, Piotr B. Mucha, Young-Pil Choi","submitted_at":"2016-09-12T15:26:05Z","abstract_excerpt":"We consider the Cucker-Smale flocking model with a singular communication weight $\\psi(s) = s^{-\\alpha}$ with $\\alpha > 0$. We provide a critical value of the exponent $\\alpha$ in the communication weight leading to global regularity of solutions or finite-time collision between particles. For $\\alpha \\geq 1$, we show that there is no collision between particles in finite time if they are placed in different positions initially. For $\\alpha\\geq 2$ we investigate a version of the Cucker-Smale model with expanded singularity i.e. with weight $\\psi_\\delta(s) = (s-\\delta)^{-\\alpha}$, $\\delta\\geq 0"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03447","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1609.03447","created_at":"2026-05-18T01:04:46.931732+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.03447v1","created_at":"2026-05-18T01:04:46.931732+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03447","created_at":"2026-05-18T01:04:46.931732+00:00"},{"alias_kind":"pith_short_12","alias_value":"KSAZQWCL3QLP","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"KSAZQWCL3QLPDIST","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"KSAZQWCL","created_at":"2026-05-18T12:30:29.479603+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KSAZQWCL3QLPDIST4VVP6VM7PC","json":"https://pith.science/pith/KSAZQWCL3QLPDIST4VVP6VM7PC.json","graph_json":"https://pith.science/api/pith-number/KSAZQWCL3QLPDIST4VVP6VM7PC/graph.json","events_json":"https://pith.science/api/pith-number/KSAZQWCL3QLPDIST4VVP6VM7PC/events.json","paper":"https://pith.science/paper/KSAZQWCL"},"agent_actions":{"view_html":"https://pith.science/pith/KSAZQWCL3QLPDIST4VVP6VM7PC","download_json":"https://pith.science/pith/KSAZQWCL3QLPDIST4VVP6VM7PC.json","view_paper":"https://pith.science/paper/KSAZQWCL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.03447&json=true","fetch_graph":"https://pith.science/api/pith-number/KSAZQWCL3QLPDIST4VVP6VM7PC/graph.json","fetch_events":"https://pith.science/api/pith-number/KSAZQWCL3QLPDIST4VVP6VM7PC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KSAZQWCL3QLPDIST4VVP6VM7PC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KSAZQWCL3QLPDIST4VVP6VM7PC/action/storage_attestation","attest_author":"https://pith.science/pith/KSAZQWCL3QLPDIST4VVP6VM7PC/action/author_attestation","sign_citation":"https://pith.science/pith/KSAZQWCL3QLPDIST4VVP6VM7PC/action/citation_signature","submit_replication":"https://pith.science/pith/KSAZQWCL3QLPDIST4VVP6VM7PC/action/replication_record"}},"created_at":"2026-05-18T01:04:46.931732+00:00","updated_at":"2026-05-18T01:04:46.931732+00:00"}