{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:7VLK6XGF2VXR4UFCYNNNXKHACM","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":"757dbd9bb55ed92ae67f383e8dc7b4d4c3133a31eb736ea4abd274e1148b3c4f","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2006-01-20T17:52:35Z","title_canon_sha256":"bd7034570a2e663c6ce6eaba31275128746a38cb4ac31ab6cd66f659b9b4f79d"},"schema_version":"1.0","source":{"id":"math/0601505","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0601505","created_at":"2026-07-04T15:52:43Z"},{"alias_kind":"arxiv_version","alias_value":"math/0601505v2","created_at":"2026-07-04T15:52:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0601505","created_at":"2026-07-04T15:52:43Z"},{"alias_kind":"pith_short_12","alias_value":"7VLK6XGF2VXR","created_at":"2026-07-04T15:52:43Z"},{"alias_kind":"pith_short_16","alias_value":"7VLK6XGF2VXR4UFC","created_at":"2026-07-04T15:52:43Z"},{"alias_kind":"pith_short_8","alias_value":"7VLK6XGF","created_at":"2026-07-04T15:52:43Z"}],"graph_snapshots":[{"event_id":"sha256:25ad16747a8d8806b14573458334c6946ca00ad1002329d5983a236d85ae849f","target":"graph","created_at":"2026-07-04T15:52:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0601505/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a new method of proving pathwise uniqueness, and we apply it to the degenerate stochastic differential equation \\[dX_t=|X_t|^{\\alpha} dW_t,\\] where $W_t$ is a one-dimensional Brownian motion and $\\alpha\\in(0,1/2)$. Weak uniqueness does not hold for the solution to this equation. If one restricts attention, however, to those solutions that spend zero time at 0, then pathwise uniqueness does hold and a strong solution exists. We also consider a class of stochastic differential equations with reflection.","authors_text":"Krzysztof Burdzy, Richard F. Bass, Zhen-Qing Chen","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2006-01-20T17:52:35Z","title":"Pathwise uniqueness for a degenerate stochastic differential equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0601505","kind":"arxiv","version":2},"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":"sha256:4c378e8f4668dc9d0ae134b8f4e3e7fc7f950d836f5c45ac2f67d647748deab7","target":"record","created_at":"2026-07-04T15:52:43Z","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":"757dbd9bb55ed92ae67f383e8dc7b4d4c3133a31eb736ea4abd274e1148b3c4f","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2006-01-20T17:52:35Z","title_canon_sha256":"bd7034570a2e663c6ce6eaba31275128746a38cb4ac31ab6cd66f659b9b4f79d"},"schema_version":"1.0","source":{"id":"math/0601505","kind":"arxiv","version":2}},"canonical_sha256":"fd56af5cc5d56f1e50a2c35adba8e0131efceb705a75e6b5e875a037ea947d44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd56af5cc5d56f1e50a2c35adba8e0131efceb705a75e6b5e875a037ea947d44","first_computed_at":"2026-07-04T15:52:43.150930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:52:43.150930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HzBXqtGh71LRbCYILSQiwGtcHBuqqLXTQuh0htqrtOSfdk3cV4jxQcaYNA9frdktwKqitvGPg4Xyi3hzJU5nCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:52:43.151280Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0601505","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c378e8f4668dc9d0ae134b8f4e3e7fc7f950d836f5c45ac2f67d647748deab7","sha256:25ad16747a8d8806b14573458334c6946ca00ad1002329d5983a236d85ae849f"],"state_sha256":"551be79c946a384d68e74304e5e9ebf49c17e25e5688f6f651edbc2829711d55"}