{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MZT6FKAZZOXCCWC6NLUOF3SV3H","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":"9aa944fb9712c50c3180202698fe778ea3054bf6cd162e283f06268966e52057","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-01T13:11:08Z","title_canon_sha256":"c34da172f8b9bb0705f917f17eb8103ca94d159764e52ee07c29bcdc92b9203b"},"schema_version":"1.0","source":{"id":"1507.00218","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00218","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00218v3","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00218","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"pith_short_12","alias_value":"MZT6FKAZZOXC","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MZT6FKAZZOXCCWC6","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MZT6FKAZ","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:13b701c45ca0e3dfe408e9977c3eba87ed5ab768b4102b5adaec7b11687fced3","target":"graph","created_at":"2026-05-18T01:30:42Z","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":"SLE$_{\\kappa}(\\rho)$ is a variant of SLE$_{\\kappa}$ where $\\rho$ characterizes the repulsion (if $\\rho>0$) or attraction $(\\rho<0)$ from the boundary. This paper examines the probabilities of SLE$_{\\kappa}(\\rho)$ to get close to the boundary. We show how close the chordal SLE$_{\\kappa}(\\rho)$ curves get to the boundary asymptotically, and provide an estimate for the probability that the SLE$_{\\kappa}(\\rho)$ curve hits graph of functions. These generalize the similar result derived by Schramm and Zhou for standard SLE$_{\\kappa}$ curves.","authors_text":"Hao Wu, Menglu Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-01T13:11:08Z","title":"Remarks on the intersection of SLE$_{\\kappa}(\\rho)$ curve with the real line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00218","kind":"arxiv","version":3},"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":"sha256:27a47ece9180f8bd22a9a8e5f59d311c19411fec8a072d6a8d577819654b574c","target":"record","created_at":"2026-05-18T01:30:42Z","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":"9aa944fb9712c50c3180202698fe778ea3054bf6cd162e283f06268966e52057","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-01T13:11:08Z","title_canon_sha256":"c34da172f8b9bb0705f917f17eb8103ca94d159764e52ee07c29bcdc92b9203b"},"schema_version":"1.0","source":{"id":"1507.00218","kind":"arxiv","version":3}},"canonical_sha256":"6667e2a819cbae21585e6ae8e2ee55d9c529e5d18ac1b73e1d62f99d4683a3fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6667e2a819cbae21585e6ae8e2ee55d9c529e5d18ac1b73e1d62f99d4683a3fa","first_computed_at":"2026-05-18T01:30:42.698114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:42.698114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t03RGideS59XA+PgP93jyS1TXuF9OMzSaDMG9/rPiRvSX9kae2KAspjShmW6KwHjnEOjXiWtjH+XQnaqaYYMCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:42.698844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.00218","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27a47ece9180f8bd22a9a8e5f59d311c19411fec8a072d6a8d577819654b574c","sha256:13b701c45ca0e3dfe408e9977c3eba87ed5ab768b4102b5adaec7b11687fced3"],"state_sha256":"ece3a86a34bac932bff3c0310705df4c2d593cbeffd1b4d42535d80b6719f65e"}