{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:YMKGZB66NEYKHKYVN3KKFAWUP4","short_pith_number":"pith:YMKGZB66","schema_version":"1.0","canonical_sha256":"c3146c87de6930a3ab156ed4a282d47f1ea599f9d6e2a23e0bf64d86ee5884b9","source":{"kind":"arxiv","id":"1802.06010","version":3},"attestation_state":"computed","paper":{"title":"Hitting Probabilities of a Brownian flow with Radial Drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Carl Mueller, Eyal Neuman, Jong Jun Lee","submitted_at":"2018-02-16T16:15:34Z","abstract_excerpt":"We consider a stochastic flow $\\phi_t(x,\\omega)$ in $\\mathbb{R}^n$ with initial point $\\phi_0(x,\\omega)=x$, driven by a single $n$-dimensional Brownian motion, and with an outward radial drift of magnitude $\\frac{ F(\\|\\phi_t(x)\\|)}{\\|\\phi_t(x)\\|}$, with $F$ nonnegative, bounded and Lipschitz. We consider initial points $x$ lying in a set of positive distance from the origin. We show that there exist constants $C^*,c^*>0$ not depending on $n$, such that if $F>C^*n$ then the image of the initial set under the flow has probability 0 of hitting the origin. If $0\\leq F \\leq c^*n^{3/4}$, and if the "},"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":"1802.06010","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-02-16T16:15:34Z","cross_cats_sorted":[],"title_canon_sha256":"89061d58ad0b5d4345d96fe260d3e3ba6a1b2d61f6ced8d62129474a493ad17c","abstract_canon_sha256":"ed2f45b81cf0634576992d096b18c90c25d91e405d5437e052cf4c174d41bc88"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:59.733640Z","signature_b64":"5FkpDWB3kbsW5Bn8A5xOm+UOYVQhrPxY2hoDQseHCIoszj+axRSFd3S2dAm0z6gzZAdQc7Y8FdVL2NjH7EwDCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3146c87de6930a3ab156ed4a282d47f1ea599f9d6e2a23e0bf64d86ee5884b9","last_reissued_at":"2026-05-17T23:49:59.732917Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:59.732917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hitting Probabilities of a Brownian flow with Radial Drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Carl Mueller, Eyal Neuman, Jong Jun Lee","submitted_at":"2018-02-16T16:15:34Z","abstract_excerpt":"We consider a stochastic flow $\\phi_t(x,\\omega)$ in $\\mathbb{R}^n$ with initial point $\\phi_0(x,\\omega)=x$, driven by a single $n$-dimensional Brownian motion, and with an outward radial drift of magnitude $\\frac{ F(\\|\\phi_t(x)\\|)}{\\|\\phi_t(x)\\|}$, with $F$ nonnegative, bounded and Lipschitz. We consider initial points $x$ lying in a set of positive distance from the origin. We show that there exist constants $C^*,c^*>0$ not depending on $n$, such that if $F>C^*n$ then the image of the initial set under the flow has probability 0 of hitting the origin. If $0\\leq F \\leq c^*n^{3/4}$, and if the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06010","kind":"arxiv","version":3},"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":"1802.06010","created_at":"2026-05-17T23:49:59.733040+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.06010v3","created_at":"2026-05-17T23:49:59.733040+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06010","created_at":"2026-05-17T23:49:59.733040+00:00"},{"alias_kind":"pith_short_12","alias_value":"YMKGZB66NEYK","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"YMKGZB66NEYKHKYV","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"YMKGZB66","created_at":"2026-05-18T12:33:04.347982+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/YMKGZB66NEYKHKYVN3KKFAWUP4","json":"https://pith.science/pith/YMKGZB66NEYKHKYVN3KKFAWUP4.json","graph_json":"https://pith.science/api/pith-number/YMKGZB66NEYKHKYVN3KKFAWUP4/graph.json","events_json":"https://pith.science/api/pith-number/YMKGZB66NEYKHKYVN3KKFAWUP4/events.json","paper":"https://pith.science/paper/YMKGZB66"},"agent_actions":{"view_html":"https://pith.science/pith/YMKGZB66NEYKHKYVN3KKFAWUP4","download_json":"https://pith.science/pith/YMKGZB66NEYKHKYVN3KKFAWUP4.json","view_paper":"https://pith.science/paper/YMKGZB66","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.06010&json=true","fetch_graph":"https://pith.science/api/pith-number/YMKGZB66NEYKHKYVN3KKFAWUP4/graph.json","fetch_events":"https://pith.science/api/pith-number/YMKGZB66NEYKHKYVN3KKFAWUP4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YMKGZB66NEYKHKYVN3KKFAWUP4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YMKGZB66NEYKHKYVN3KKFAWUP4/action/storage_attestation","attest_author":"https://pith.science/pith/YMKGZB66NEYKHKYVN3KKFAWUP4/action/author_attestation","sign_citation":"https://pith.science/pith/YMKGZB66NEYKHKYVN3KKFAWUP4/action/citation_signature","submit_replication":"https://pith.science/pith/YMKGZB66NEYKHKYVN3KKFAWUP4/action/replication_record"}},"created_at":"2026-05-17T23:49:59.733040+00:00","updated_at":"2026-05-17T23:49:59.733040+00:00"}