{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:BRIUGIE5LLE4DY473K4V5W7QXH","short_pith_number":"pith:BRIUGIE5","schema_version":"1.0","canonical_sha256":"0c5143209d5ac9c1e39fdab95edbf0b9f182610ea72f0a3b36cff390b009d099","source":{"kind":"arxiv","id":"1108.3992","version":5},"attestation_state":"computed","paper":{"title":"Planar Diffusions with Rank-Based Characteristics: Transition Probabilities, Time Reversal, Maximality and Perturbed Tanaka equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"E. Robert Fernholz, Ioannis Karatzas, Tomoyuki Ichiba, Vilmos Prokaj","submitted_at":"2011-08-19T16:07:57Z","abstract_excerpt":"We construct a planar diffusion process whose infinitesimal generator depends only on the order of the components of the process. Speaking informally and a bit imprecisely for the moment, imagine you run two Brownian-like particles on the real line. At any given time, you assign positive drift g and diffusion {\\sigma} to the laggard; and you assign negative drift -h and diffusion {\\rho} to the leader.\n  We compute the transition probabilities of this process, discuss its realization in terms of appropriate systems of stochastic differential equations, study its dynamics under a time reversal, "},"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":"1108.3992","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-19T16:07:57Z","cross_cats_sorted":[],"title_canon_sha256":"8f16e02c55227fb52d39e516fed67f980f8cb93118ed4e622288185933bc8646","abstract_canon_sha256":"8b8b4b30f0c981c9b44b14304964c06f917c3dab627eb1d1cbfa7173e4b8dac7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:20.408637Z","signature_b64":"JrfP7+2CSb4l15OgePQBvpZ987NL5O0DofcEiVIGNfpTMKfG2YU5DKKU1Gsejy6dhTfCOQqSFWlwgIgDhWuvDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c5143209d5ac9c1e39fdab95edbf0b9f182610ea72f0a3b36cff390b009d099","last_reissued_at":"2026-05-18T03:53:20.408006Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:20.408006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Planar Diffusions with Rank-Based Characteristics: Transition Probabilities, Time Reversal, Maximality and Perturbed Tanaka equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"E. Robert Fernholz, Ioannis Karatzas, Tomoyuki Ichiba, Vilmos Prokaj","submitted_at":"2011-08-19T16:07:57Z","abstract_excerpt":"We construct a planar diffusion process whose infinitesimal generator depends only on the order of the components of the process. Speaking informally and a bit imprecisely for the moment, imagine you run two Brownian-like particles on the real line. At any given time, you assign positive drift g and diffusion {\\sigma} to the laggard; and you assign negative drift -h and diffusion {\\rho} to the leader.\n  We compute the transition probabilities of this process, discuss its realization in terms of appropriate systems of stochastic differential equations, study its dynamics under a time reversal, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3992","kind":"arxiv","version":5},"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":"1108.3992","created_at":"2026-05-18T03:53:20.408126+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.3992v5","created_at":"2026-05-18T03:53:20.408126+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3992","created_at":"2026-05-18T03:53:20.408126+00:00"},{"alias_kind":"pith_short_12","alias_value":"BRIUGIE5LLE4","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BRIUGIE5LLE4DY47","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BRIUGIE5","created_at":"2026-05-18T12:26:24.575870+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/BRIUGIE5LLE4DY473K4V5W7QXH","json":"https://pith.science/pith/BRIUGIE5LLE4DY473K4V5W7QXH.json","graph_json":"https://pith.science/api/pith-number/BRIUGIE5LLE4DY473K4V5W7QXH/graph.json","events_json":"https://pith.science/api/pith-number/BRIUGIE5LLE4DY473K4V5W7QXH/events.json","paper":"https://pith.science/paper/BRIUGIE5"},"agent_actions":{"view_html":"https://pith.science/pith/BRIUGIE5LLE4DY473K4V5W7QXH","download_json":"https://pith.science/pith/BRIUGIE5LLE4DY473K4V5W7QXH.json","view_paper":"https://pith.science/paper/BRIUGIE5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.3992&json=true","fetch_graph":"https://pith.science/api/pith-number/BRIUGIE5LLE4DY473K4V5W7QXH/graph.json","fetch_events":"https://pith.science/api/pith-number/BRIUGIE5LLE4DY473K4V5W7QXH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BRIUGIE5LLE4DY473K4V5W7QXH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BRIUGIE5LLE4DY473K4V5W7QXH/action/storage_attestation","attest_author":"https://pith.science/pith/BRIUGIE5LLE4DY473K4V5W7QXH/action/author_attestation","sign_citation":"https://pith.science/pith/BRIUGIE5LLE4DY473K4V5W7QXH/action/citation_signature","submit_replication":"https://pith.science/pith/BRIUGIE5LLE4DY473K4V5W7QXH/action/replication_record"}},"created_at":"2026-05-18T03:53:20.408126+00:00","updated_at":"2026-05-18T03:53:20.408126+00:00"}