{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KSAZQWCL3QLPDIST4VVP6VM7PC","short_pith_number":"pith:KSAZQWCL","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"},"canonical_sha256":"548198584bdc16f1a253e56aff559f7888b7b93b5e17a5d887314c86c3afb252","source":{"kind":"arxiv","id":"1609.03447","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03447","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03447v1","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03447","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"pith_short_12","alias_value":"KSAZQWCL3QLP","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KSAZQWCL3QLPDIST","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KSAZQWCL","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KSAZQWCL3QLPDIST4VVP6VM7PC","target":"record","payload":{"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"},"canonical_sha256":"548198584bdc16f1a253e56aff559f7888b7b93b5e17a5d887314c86c3afb252","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"},"source_kind":"arxiv","source_id":"1609.03447","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":"2026-05-18T01:04:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Unv7ADEdSjWRii5e/BPQI7+IdwaApnVp588z8xr+xtVd2mMPzNS7teN+7K663eeyS7Z7+eP4ycOGgmUwwfwDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T00:50:33.605983Z"},"content_sha256":"b9a0afdfe14bc6494e0eb908d5b3a18ba4c072a89cd54606558d44aa77d0ca10","schema_version":"1.0","event_id":"sha256:b9a0afdfe14bc6494e0eb908d5b3a18ba4c072a89cd54606558d44aa77d0ca10"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KSAZQWCL3QLPDIST4VVP6VM7PC","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l5NGN3boKvY/ThECn5/PVn1582axlU3dvh4jR9xYB3JLAv+6ej1BqQmxI3n4LHn6KXyXeSXLSOnt7ftLtsOxDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T00:50:33.606354Z"},"content_sha256":"88644104441804830153d5cc900069f00a723348b5d7dff94fb14ecaef63b9e9","schema_version":"1.0","event_id":"sha256:88644104441804830153d5cc900069f00a723348b5d7dff94fb14ecaef63b9e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KSAZQWCL3QLPDIST4VVP6VM7PC/bundle.json","state_url":"https://pith.science/pith/KSAZQWCL3QLPDIST4VVP6VM7PC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KSAZQWCL3QLPDIST4VVP6VM7PC/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":"2026-06-04T00:50:33Z","links":{"resolver":"https://pith.science/pith/KSAZQWCL3QLPDIST4VVP6VM7PC","bundle":"https://pith.science/pith/KSAZQWCL3QLPDIST4VVP6VM7PC/bundle.json","state":"https://pith.science/pith/KSAZQWCL3QLPDIST4VVP6VM7PC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KSAZQWCL3QLPDIST4VVP6VM7PC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KSAZQWCL3QLPDIST4VVP6VM7PC","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":"6f83af68cf832c7a9312b7f94d695339bdab06f40828e8ea9827faa9ef2c2451","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-12T15:26:05Z","title_canon_sha256":"e6cc9c8a31763a20b4bd7ecbc301c1a5a896f9c5898dd1280c687bd61fe64547"},"schema_version":"1.0","source":{"id":"1609.03447","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03447","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03447v1","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03447","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"pith_short_12","alias_value":"KSAZQWCL3QLP","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KSAZQWCL3QLPDIST","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KSAZQWCL","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:88644104441804830153d5cc900069f00a723348b5d7dff94fb14ecaef63b9e9","target":"graph","created_at":"2026-05-18T01:04:46Z","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 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","authors_text":"Jan Peszek, Jose A. Carrillo, Piotr B. Mucha, Young-Pil Choi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-12T15:26:05Z","title":"Sharp conditions to avoid collisions in singular Cucker-Smale interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03447","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:b9a0afdfe14bc6494e0eb908d5b3a18ba4c072a89cd54606558d44aa77d0ca10","target":"record","created_at":"2026-05-18T01:04:46Z","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":"6f83af68cf832c7a9312b7f94d695339bdab06f40828e8ea9827faa9ef2c2451","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-12T15:26:05Z","title_canon_sha256":"e6cc9c8a31763a20b4bd7ecbc301c1a5a896f9c5898dd1280c687bd61fe64547"},"schema_version":"1.0","source":{"id":"1609.03447","kind":"arxiv","version":1}},"canonical_sha256":"548198584bdc16f1a253e56aff559f7888b7b93b5e17a5d887314c86c3afb252","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"548198584bdc16f1a253e56aff559f7888b7b93b5e17a5d887314c86c3afb252","first_computed_at":"2026-05-18T01:04:46.931632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:46.931632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sXPNiwm6Rh7FtihpIV/T0JYFYKB4wUcCMRDBH0Y5wOophd5SO1cwhA/T5HylbdIGii8Ie2OYwZJYJ6N63h9XBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:46.932293Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03447","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9a0afdfe14bc6494e0eb908d5b3a18ba4c072a89cd54606558d44aa77d0ca10","sha256:88644104441804830153d5cc900069f00a723348b5d7dff94fb14ecaef63b9e9"],"state_sha256":"95ed733bea60f7917ce4e022d6dffdd5236a2493a8a6edeb8dce5abcacd4935d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JWs2enHoeaxNB5IKmsQkSVE5KunpJ+6x1viMdjuCVm7qRcE3DS/jgnyLBjIDR/vNAn6yRHBdxVxKELdPKBwqAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T00:50:33.609367Z","bundle_sha256":"b149c22cdfbe34cc7be8ccf4284974a768902908f7012060918094837f91db3f"}}