{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MZT6FKAZZOXCCWC6NLUOF3SV3H","short_pith_number":"pith:MZT6FKAZ","canonical_record":{"source":{"id":"1507.00218","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-01T13:11:08Z","cross_cats_sorted":[],"title_canon_sha256":"c34da172f8b9bb0705f917f17eb8103ca94d159764e52ee07c29bcdc92b9203b","abstract_canon_sha256":"9aa944fb9712c50c3180202698fe778ea3054bf6cd162e283f06268966e52057"},"schema_version":"1.0"},"canonical_sha256":"6667e2a819cbae21585e6ae8e2ee55d9c529e5d18ac1b73e1d62f99d4683a3fa","source":{"kind":"arxiv","id":"1507.00218","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MZT6FKAZZOXCCWC6NLUOF3SV3H","target":"record","payload":{"canonical_record":{"source":{"id":"1507.00218","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-01T13:11:08Z","cross_cats_sorted":[],"title_canon_sha256":"c34da172f8b9bb0705f917f17eb8103ca94d159764e52ee07c29bcdc92b9203b","abstract_canon_sha256":"9aa944fb9712c50c3180202698fe778ea3054bf6cd162e283f06268966e52057"},"schema_version":"1.0"},"canonical_sha256":"6667e2a819cbae21585e6ae8e2ee55d9c529e5d18ac1b73e1d62f99d4683a3fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:42.698844Z","signature_b64":"t03RGideS59XA+PgP93jyS1TXuF9OMzSaDMG9/rPiRvSX9kae2KAspjShmW6KwHjnEOjXiWtjH+XQnaqaYYMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6667e2a819cbae21585e6ae8e2ee55d9c529e5d18ac1b73e1d62f99d4683a3fa","last_reissued_at":"2026-05-18T01:30:42.698114Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:42.698114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.00218","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KqJbCFUs7c3pxaLPbgqmlrVD4/sBjSbzkunRHEHzByXF0wkrsq3DVumTCS4df44AQCe2AHiLZPbghaxdLQIJDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:23:16.987277Z"},"content_sha256":"27a47ece9180f8bd22a9a8e5f59d311c19411fec8a072d6a8d577819654b574c","schema_version":"1.0","event_id":"sha256:27a47ece9180f8bd22a9a8e5f59d311c19411fec8a072d6a8d577819654b574c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MZT6FKAZZOXCCWC6NLUOF3SV3H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Remarks on the intersection of SLE$_{\\kappa}(\\rho)$ curve with the real line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hao Wu, Menglu Wang","submitted_at":"2015-07-01T13:11:08Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00218","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sfSoGw5qPyY16IBKSoP8afe+HNggGjKsEKn/iEBbwa27Hj9aGDDiL3GuOAf1+0LvdXOVJE9oINCFsU5hzGYjCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:23:16.988000Z"},"content_sha256":"13b701c45ca0e3dfe408e9977c3eba87ed5ab768b4102b5adaec7b11687fced3","schema_version":"1.0","event_id":"sha256:13b701c45ca0e3dfe408e9977c3eba87ed5ab768b4102b5adaec7b11687fced3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MZT6FKAZZOXCCWC6NLUOF3SV3H/bundle.json","state_url":"https://pith.science/pith/MZT6FKAZZOXCCWC6NLUOF3SV3H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MZT6FKAZZOXCCWC6NLUOF3SV3H/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":"2026-05-25T18:23:16Z","links":{"resolver":"https://pith.science/pith/MZT6FKAZZOXCCWC6NLUOF3SV3H","bundle":"https://pith.science/pith/MZT6FKAZZOXCCWC6NLUOF3SV3H/bundle.json","state":"https://pith.science/pith/MZT6FKAZZOXCCWC6NLUOF3SV3H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MZT6FKAZZOXCCWC6NLUOF3SV3H/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oR0Cdd2gQuleCXjtQaWtbLojnWIXBgGvMiTA3RCdZYiv0CaRg3eJjpjr/fRKM2mz2WN9ZMvRoABzWBb/P4dWDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T18:23:16.991600Z","bundle_sha256":"906623368647e0d0eec80244c96aa2049ba1d74bbc927c27fbe7d4eca12aa57f"}}