{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4JVPARPLZBAJMPY5KPOG2EE5UW","short_pith_number":"pith:4JVPARPL","canonical_record":{"source":{"id":"1711.10371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-28T16:09:32Z","cross_cats_sorted":[],"title_canon_sha256":"167625aff0f3abd848b3cdf03f691295c78b775ac6b0646699bd2d2b0d5c16c1","abstract_canon_sha256":"7e150d090ecc303235805e5c3af538979e262f4a8bdb97dd21c68fb6d9b4cfe9"},"schema_version":"1.0"},"canonical_sha256":"e26af045ebc840963f1d53dc6d109da59faff5ad0582f42870858d5889f8891b","source":{"kind":"arxiv","id":"1711.10371","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.10371","created_at":"2026-05-18T00:29:22Z"},{"alias_kind":"arxiv_version","alias_value":"1711.10371v1","created_at":"2026-05-18T00:29:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10371","created_at":"2026-05-18T00:29:22Z"},{"alias_kind":"pith_short_12","alias_value":"4JVPARPLZBAJ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4JVPARPLZBAJMPY5","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4JVPARPL","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4JVPARPLZBAJMPY5KPOG2EE5UW","target":"record","payload":{"canonical_record":{"source":{"id":"1711.10371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-28T16:09:32Z","cross_cats_sorted":[],"title_canon_sha256":"167625aff0f3abd848b3cdf03f691295c78b775ac6b0646699bd2d2b0d5c16c1","abstract_canon_sha256":"7e150d090ecc303235805e5c3af538979e262f4a8bdb97dd21c68fb6d9b4cfe9"},"schema_version":"1.0"},"canonical_sha256":"e26af045ebc840963f1d53dc6d109da59faff5ad0582f42870858d5889f8891b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:22.385001Z","signature_b64":"Oq6XWpsyKFwthDOwor9lKh8hPjtkaG41v7pBaU/XU4Uvi8zPF462EfGzGYA04vyU8k9wk0aESukIjY5f6povAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e26af045ebc840963f1d53dc6d109da59faff5ad0582f42870858d5889f8891b","last_reissued_at":"2026-05-18T00:29:22.384243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:22.384243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.10371","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":"2026-05-18T00:29:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xSxm9RLAp6rIzfr3+vx2dO9gTxJIoVDHvHbuBgfHqKo8tLGK1J9pn9dqo6URUbk50R3IbrWaEP6OX2fGVflBCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:03:28.630091Z"},"content_sha256":"3060345d0e034b962245a08f8e9eff47472e0bfba9d91425672e3b3fc6537b31","schema_version":"1.0","event_id":"sha256:3060345d0e034b962245a08f8e9eff47472e0bfba9d91425672e3b3fc6537b31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4JVPARPLZBAJMPY5KPOG2EE5UW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cucker-Smale flocking particles with multiplicative noises: stochastic mean-field limit and phase transition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Samir Salem, Young-Pil Choi","submitted_at":"2017-11-28T16:09:32Z","abstract_excerpt":"In this paper, we consider the Cucker-Smale flocking particles which are subject to the same velocity-dependent noise, which exhibits a phase change phenomenon occurs bringing the system from a \"non flocking\" to a \"flocking\" state as the strength of noises decreases. We rigorously show the stochastic mean-field limit from the many-particle Cucker-Smale system with multiplicative noises to the Vlasov-type stochastic partial differential equation as the number of particles goes to infinity. More precisely, we provide a quantitative error estimate between solutions to the stochastic particle syst"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10371","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":"2026-05-18T00:29:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"onAvol2E0NZGgVdyUq8THWVnmazHdcSJbTgVWRfq0dP18n3P1hrb0vXcjCt2vtUgBbltUoSm5hR+f8PK7jOnDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:03:28.630466Z"},"content_sha256":"f8af0baa1f3f3e40e49f673af9aa1cac31f8aed21656cebf838f38f34944bcc7","schema_version":"1.0","event_id":"sha256:f8af0baa1f3f3e40e49f673af9aa1cac31f8aed21656cebf838f38f34944bcc7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4JVPARPLZBAJMPY5KPOG2EE5UW/bundle.json","state_url":"https://pith.science/pith/4JVPARPLZBAJMPY5KPOG2EE5UW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4JVPARPLZBAJMPY5KPOG2EE5UW/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":"2026-06-02T05:03:28Z","links":{"resolver":"https://pith.science/pith/4JVPARPLZBAJMPY5KPOG2EE5UW","bundle":"https://pith.science/pith/4JVPARPLZBAJMPY5KPOG2EE5UW/bundle.json","state":"https://pith.science/pith/4JVPARPLZBAJMPY5KPOG2EE5UW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4JVPARPLZBAJMPY5KPOG2EE5UW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4JVPARPLZBAJMPY5KPOG2EE5UW","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":"7e150d090ecc303235805e5c3af538979e262f4a8bdb97dd21c68fb6d9b4cfe9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-28T16:09:32Z","title_canon_sha256":"167625aff0f3abd848b3cdf03f691295c78b775ac6b0646699bd2d2b0d5c16c1"},"schema_version":"1.0","source":{"id":"1711.10371","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.10371","created_at":"2026-05-18T00:29:22Z"},{"alias_kind":"arxiv_version","alias_value":"1711.10371v1","created_at":"2026-05-18T00:29:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10371","created_at":"2026-05-18T00:29:22Z"},{"alias_kind":"pith_short_12","alias_value":"4JVPARPLZBAJ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4JVPARPLZBAJMPY5","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4JVPARPL","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:f8af0baa1f3f3e40e49f673af9aa1cac31f8aed21656cebf838f38f34944bcc7","target":"graph","created_at":"2026-05-18T00:29:22Z","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 paper, we consider the Cucker-Smale flocking particles which are subject to the same velocity-dependent noise, which exhibits a phase change phenomenon occurs bringing the system from a \"non flocking\" to a \"flocking\" state as the strength of noises decreases. We rigorously show the stochastic mean-field limit from the many-particle Cucker-Smale system with multiplicative noises to the Vlasov-type stochastic partial differential equation as the number of particles goes to infinity. More precisely, we provide a quantitative error estimate between solutions to the stochastic particle syst","authors_text":"Samir Salem, Young-Pil Choi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-28T16:09:32Z","title":"Cucker-Smale flocking particles with multiplicative noises: stochastic mean-field limit and phase transition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10371","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":"sha256:3060345d0e034b962245a08f8e9eff47472e0bfba9d91425672e3b3fc6537b31","target":"record","created_at":"2026-05-18T00:29:22Z","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":"7e150d090ecc303235805e5c3af538979e262f4a8bdb97dd21c68fb6d9b4cfe9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-28T16:09:32Z","title_canon_sha256":"167625aff0f3abd848b3cdf03f691295c78b775ac6b0646699bd2d2b0d5c16c1"},"schema_version":"1.0","source":{"id":"1711.10371","kind":"arxiv","version":1}},"canonical_sha256":"e26af045ebc840963f1d53dc6d109da59faff5ad0582f42870858d5889f8891b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e26af045ebc840963f1d53dc6d109da59faff5ad0582f42870858d5889f8891b","first_computed_at":"2026-05-18T00:29:22.384243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:22.384243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Oq6XWpsyKFwthDOwor9lKh8hPjtkaG41v7pBaU/XU4Uvi8zPF462EfGzGYA04vyU8k9wk0aESukIjY5f6povAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:22.385001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.10371","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3060345d0e034b962245a08f8e9eff47472e0bfba9d91425672e3b3fc6537b31","sha256:f8af0baa1f3f3e40e49f673af9aa1cac31f8aed21656cebf838f38f34944bcc7"],"state_sha256":"b85908a6b6f22ff2841e0f13c5541292a5e35e250dd69367e02e14ddc8e7bd62"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wNSRPlHpP6m4AdgOlTJ52SlSanzrqKvo1d6FEOx4fz4GAfEUEfxa4dpZsgYrBKUzg8C1Z+ahIxNu4JkwP53zBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T05:03:28.632397Z","bundle_sha256":"f93e9348edb41e1736aa1511742144920f11c286f7bb9f18ed4d2beea2d14fe4"}}