{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:BB2NUTFV4DVRS27PXJNVVEMJ3T","short_pith_number":"pith:BB2NUTFV","canonical_record":{"source":{"id":"math/0303354","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2003-03-27T16:22:59Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e34a3f5ef6b72de3ddf3a7782e7ea737550ec99b4d0ec479dc34d2d50f853945","abstract_canon_sha256":"552fa3b27a1374f827446501b6776c0d0af8970fed27239ef1d86543e5bbe7d3"},"schema_version":"1.0"},"canonical_sha256":"0874da4cb5e0eb196befba5b5a9189dcd3eac28728ccd2a6ce4ceb9ce374ce93","source":{"kind":"arxiv","id":"math/0303354","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0303354","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"arxiv_version","alias_value":"math/0303354v1","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0303354","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"pith_short_12","alias_value":"BB2NUTFV4DVR","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"BB2NUTFV4DVRS27P","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"BB2NUTFV","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:BB2NUTFV4DVRS27PXJNVVEMJ3T","target":"record","payload":{"canonical_record":{"source":{"id":"math/0303354","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2003-03-27T16:22:59Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e34a3f5ef6b72de3ddf3a7782e7ea737550ec99b4d0ec479dc34d2d50f853945","abstract_canon_sha256":"552fa3b27a1374f827446501b6776c0d0af8970fed27239ef1d86543e5bbe7d3"},"schema_version":"1.0"},"canonical_sha256":"0874da4cb5e0eb196befba5b5a9189dcd3eac28728ccd2a6ce4ceb9ce374ce93","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:01.491139Z","signature_b64":"r6/+s5GPMovNvV/0FGu1InLdPatX8cRwSVLofSwWKFPPPD8uienYaXDAHhCmvBnD1UF0hNxrO9BRZ7/SqPUwAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0874da4cb5e0eb196befba5b5a9189dcd3eac28728ccd2a6ce4ceb9ce374ce93","last_reissued_at":"2026-05-18T00:40:01.490491Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:01.490491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0303354","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fz4kf3oB0wjtNkwNRYr+O3JU6vRoEacP0rWAIpfAJ1ROcv7J/g7yqo7YeFXCT3JJ2zZqoCNuMmvMrU0OwU6vAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:50:14.914140Z"},"content_sha256":"2ea58b1b22257bdbae1865571de97f0dfd9843fc19df32a70631ee6221c50e7a","schema_version":"1.0","event_id":"sha256:2ea58b1b22257bdbae1865571de97f0dfd9843fc19df32a70631ee6221c50e7a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:BB2NUTFV4DVRS27PXJNVVEMJ3T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random planar curves and Schramm-Loewner evolutions","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Wendelin Werner","submitted_at":"2003-03-27T16:22:59Z","abstract_excerpt":"We review some of the results that have been derived in the last years on conformal invariance, scaling limits and properties of some two-dimensional random curves. In particular, we describe the intuitive ideas that lead to the definition of the Schramm-Loewner evolutions SLE, we define these objects, study its various properties, show how to compute (probabilities, critical exponents) using SLE, relate SLE to planar Brownian motions (i.e. the determination of the critical exponents), planar self-avoiding walks, critical percolation, loop-erased random walks and uniform spanning trees."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0303354","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LQTk+a6iwG6rvoWoaQx8TyiwWBwyfWruI+4EKiQ+dyDUgrvbJLgsSxQNQbB3cT8Xv5WlmLjZdhHBHQuq1cKQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:50:14.914542Z"},"content_sha256":"70207a47c22a3069118f6f1a1c71207e3522bd5d18c7af65241e19e93da9d9ea","schema_version":"1.0","event_id":"sha256:70207a47c22a3069118f6f1a1c71207e3522bd5d18c7af65241e19e93da9d9ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BB2NUTFV4DVRS27PXJNVVEMJ3T/bundle.json","state_url":"https://pith.science/pith/BB2NUTFV4DVRS27PXJNVVEMJ3T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BB2NUTFV4DVRS27PXJNVVEMJ3T/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":"2026-05-31T04:50:14Z","links":{"resolver":"https://pith.science/pith/BB2NUTFV4DVRS27PXJNVVEMJ3T","bundle":"https://pith.science/pith/BB2NUTFV4DVRS27PXJNVVEMJ3T/bundle.json","state":"https://pith.science/pith/BB2NUTFV4DVRS27PXJNVVEMJ3T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BB2NUTFV4DVRS27PXJNVVEMJ3T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:BB2NUTFV4DVRS27PXJNVVEMJ3T","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":"552fa3b27a1374f827446501b6776c0d0af8970fed27239ef1d86543e5bbe7d3","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.PR","submitted_at":"2003-03-27T16:22:59Z","title_canon_sha256":"e34a3f5ef6b72de3ddf3a7782e7ea737550ec99b4d0ec479dc34d2d50f853945"},"schema_version":"1.0","source":{"id":"math/0303354","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0303354","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"arxiv_version","alias_value":"math/0303354v1","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0303354","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"pith_short_12","alias_value":"BB2NUTFV4DVR","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"BB2NUTFV4DVRS27P","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"BB2NUTFV","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:70207a47c22a3069118f6f1a1c71207e3522bd5d18c7af65241e19e93da9d9ea","target":"graph","created_at":"2026-05-18T00:40:01Z","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":"We review some of the results that have been derived in the last years on conformal invariance, scaling limits and properties of some two-dimensional random curves. In particular, we describe the intuitive ideas that lead to the definition of the Schramm-Loewner evolutions SLE, we define these objects, study its various properties, show how to compute (probabilities, critical exponents) using SLE, relate SLE to planar Brownian motions (i.e. the determination of the critical exponents), planar self-avoiding walks, critical percolation, loop-erased random walks and uniform spanning trees.","authors_text":"Wendelin Werner","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2003-03-27T16:22:59Z","title":"Random planar curves and Schramm-Loewner evolutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0303354","kind":"arxiv","version":1},"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":"sha256:2ea58b1b22257bdbae1865571de97f0dfd9843fc19df32a70631ee6221c50e7a","target":"record","created_at":"2026-05-18T00:40:01Z","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":"552fa3b27a1374f827446501b6776c0d0af8970fed27239ef1d86543e5bbe7d3","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.PR","submitted_at":"2003-03-27T16:22:59Z","title_canon_sha256":"e34a3f5ef6b72de3ddf3a7782e7ea737550ec99b4d0ec479dc34d2d50f853945"},"schema_version":"1.0","source":{"id":"math/0303354","kind":"arxiv","version":1}},"canonical_sha256":"0874da4cb5e0eb196befba5b5a9189dcd3eac28728ccd2a6ce4ceb9ce374ce93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0874da4cb5e0eb196befba5b5a9189dcd3eac28728ccd2a6ce4ceb9ce374ce93","first_computed_at":"2026-05-18T00:40:01.490491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:01.490491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r6/+s5GPMovNvV/0FGu1InLdPatX8cRwSVLofSwWKFPPPD8uienYaXDAHhCmvBnD1UF0hNxrO9BRZ7/SqPUwAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:01.491139Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0303354","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ea58b1b22257bdbae1865571de97f0dfd9843fc19df32a70631ee6221c50e7a","sha256:70207a47c22a3069118f6f1a1c71207e3522bd5d18c7af65241e19e93da9d9ea"],"state_sha256":"bea3c4d7f3b96b104a9642ecdfa513602eb1b48414f95fe6722d8d062c4ce325"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ZnPCVz4xk8Dte4V3IEm18LRE4+lKPPG1CYlRj6Uq6iyPCfKiwLZc650MCXuTOHVZHtrVxhdekJWpHB8e5OlBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:50:14.918117Z","bundle_sha256":"fcc09132c1e16c7a337930cffb152a78ce4dbe9c658a8ccaabf1e96f6bf47bca"}}