{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:BAMU7GFHCXG3C7JVMPVJ675NAO","short_pith_number":"pith:BAMU7GFH","schema_version":"1.0","canonical_sha256":"08194f98a715cdb17d3563ea9f7fad03b5d0772d2f90cefa23d5d5e5eccbaf27","source":{"kind":"arxiv","id":"1109.2328","version":1},"attestation_state":"computed","paper":{"title":"Restriction Properties of Annulus SLE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dapeng Zhan","submitted_at":"2011-09-11T16:57:26Z","abstract_excerpt":"For $\\kappa\\in(0,4]$, a family of annulus SLE$(\\kappa;\\Lambda)$ processes were introduced in [14] to prove the reversibility of whole-plane SLE$(\\kappa)$. In this paper we prove that those annulus SLE$(\\kappa;\\Lambda)$ processes satisfy a restriction property, which is similar to that for chordal SLE$(\\kappa)$. Using this property, we construct $n\\ge 2$ curves crossing an annulus such that, when any $n-1$ curves are given, the last curve is a chordal SLE$(\\kappa)$ trace."},"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":"1109.2328","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-09-11T16:57:26Z","cross_cats_sorted":[],"title_canon_sha256":"f082da41a9000ed0e66cc6ac6ea97f273f725638e50ef861b7f55260d91e7442","abstract_canon_sha256":"edae87e7f9fe319ebd92764d1afd457b165addfbfa92143d95e3e94bfb5af249"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:34.730149Z","signature_b64":"hM6Jst3Hxo3NWSwVgAe/K2SOYeFbPHZswS6veepHIV7BF9lnLHNMrMLg0arOkkt4hlTqjldm7/1LmXDSLQUhAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08194f98a715cdb17d3563ea9f7fad03b5d0772d2f90cefa23d5d5e5eccbaf27","last_reissued_at":"2026-05-18T02:00:34.729592Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:34.729592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Restriction Properties of Annulus SLE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dapeng Zhan","submitted_at":"2011-09-11T16:57:26Z","abstract_excerpt":"For $\\kappa\\in(0,4]$, a family of annulus SLE$(\\kappa;\\Lambda)$ processes were introduced in [14] to prove the reversibility of whole-plane SLE$(\\kappa)$. In this paper we prove that those annulus SLE$(\\kappa;\\Lambda)$ processes satisfy a restriction property, which is similar to that for chordal SLE$(\\kappa)$. Using this property, we construct $n\\ge 2$ curves crossing an annulus such that, when any $n-1$ curves are given, the last curve is a chordal SLE$(\\kappa)$ trace."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2328","kind":"arxiv","version":1},"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":"1109.2328","created_at":"2026-05-18T02:00:34.729682+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.2328v1","created_at":"2026-05-18T02:00:34.729682+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2328","created_at":"2026-05-18T02:00:34.729682+00:00"},{"alias_kind":"pith_short_12","alias_value":"BAMU7GFHCXG3","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BAMU7GFHCXG3C7JV","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BAMU7GFH","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/BAMU7GFHCXG3C7JVMPVJ675NAO","json":"https://pith.science/pith/BAMU7GFHCXG3C7JVMPVJ675NAO.json","graph_json":"https://pith.science/api/pith-number/BAMU7GFHCXG3C7JVMPVJ675NAO/graph.json","events_json":"https://pith.science/api/pith-number/BAMU7GFHCXG3C7JVMPVJ675NAO/events.json","paper":"https://pith.science/paper/BAMU7GFH"},"agent_actions":{"view_html":"https://pith.science/pith/BAMU7GFHCXG3C7JVMPVJ675NAO","download_json":"https://pith.science/pith/BAMU7GFHCXG3C7JVMPVJ675NAO.json","view_paper":"https://pith.science/paper/BAMU7GFH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.2328&json=true","fetch_graph":"https://pith.science/api/pith-number/BAMU7GFHCXG3C7JVMPVJ675NAO/graph.json","fetch_events":"https://pith.science/api/pith-number/BAMU7GFHCXG3C7JVMPVJ675NAO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BAMU7GFHCXG3C7JVMPVJ675NAO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BAMU7GFHCXG3C7JVMPVJ675NAO/action/storage_attestation","attest_author":"https://pith.science/pith/BAMU7GFHCXG3C7JVMPVJ675NAO/action/author_attestation","sign_citation":"https://pith.science/pith/BAMU7GFHCXG3C7JVMPVJ675NAO/action/citation_signature","submit_replication":"https://pith.science/pith/BAMU7GFHCXG3C7JVMPVJ675NAO/action/replication_record"}},"created_at":"2026-05-18T02:00:34.729682+00:00","updated_at":"2026-05-18T02:00:34.729682+00:00"}