{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:FCC4VXALQD5PMSQYYJB33UR2V7","short_pith_number":"pith:FCC4VXAL","canonical_record":{"source":{"id":"1201.1498","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-06T20:56:04Z","cross_cats_sorted":["math-ph","math.CV","math.MP"],"title_canon_sha256":"154d52f9b439c24076f8fce57d5377a06f572b2921fe12ff3a1deaa853b88d64","abstract_canon_sha256":"bdb26a75a7a196fbb7ccf9e72a9d0150b8721bc119004e9db2ea6f3a177a51cb"},"schema_version":"1.0"},"canonical_sha256":"2885cadc0b80faf64a18c243bdd23aafcab419ea01d4c9ff9d728a00b969216e","source":{"kind":"arxiv","id":"1201.1498","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1498","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1498v2","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1498","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"pith_short_12","alias_value":"FCC4VXALQD5P","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FCC4VXALQD5PMSQY","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FCC4VXAL","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:FCC4VXALQD5PMSQYYJB33UR2V7","target":"record","payload":{"canonical_record":{"source":{"id":"1201.1498","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-06T20:56:04Z","cross_cats_sorted":["math-ph","math.CV","math.MP"],"title_canon_sha256":"154d52f9b439c24076f8fce57d5377a06f572b2921fe12ff3a1deaa853b88d64","abstract_canon_sha256":"bdb26a75a7a196fbb7ccf9e72a9d0150b8721bc119004e9db2ea6f3a177a51cb"},"schema_version":"1.0"},"canonical_sha256":"2885cadc0b80faf64a18c243bdd23aafcab419ea01d4c9ff9d728a00b969216e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:55.870252Z","signature_b64":"LZ3ZNYgUTdZq+oK4AKCQ8+wYXrNqGaEXKaVI+bYRR9ZHY779bpHargapPolw9dOPRg9HhoPBBwCJam1YUXzUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2885cadc0b80faf64a18c243bdd23aafcab419ea01d4c9ff9d728a00b969216e","last_reissued_at":"2026-05-18T01:19:55.869598Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:55.869598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.1498","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a5lAoa37lIwOwBVa37uhDolLBvv+nvwWBw0fe2oSw5IKB0TrZTeOCeEnMT7bWA9yy1h9vLLwRM53gwuwk/7YAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:02:51.708003Z"},"content_sha256":"060fe8991ac83b2ded3939788ab095abb0af4a6c4e64cd61fb1e31d009dca8bd","schema_version":"1.0","event_id":"sha256:060fe8991ac83b2ded3939788ab095abb0af4a6c4e64cd61fb1e31d009dca8bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:FCC4VXALQD5PMSQYYJB33UR2V7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Imaginary geometry III: reversibility of SLE_\\kappa\\ for \\kappa \\in (4,8)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CV","math.MP"],"primary_cat":"math.PR","authors_text":"Jason Miller, Scott Sheffield","submitted_at":"2012-01-06T20:56:04Z","abstract_excerpt":"Suppose that D is a planar Jordan domain and x and y are distinct boundary points of D. Fix \\kappa \\in (4,8) and let \\eta\\ be an SLE_\\kappa process from x to y in D. We prove that the law of the time-reversal of \\eta is, up to reparameterization, an SLE_\\kappa process from y to x in D. More generally, we prove that SLE_\\kappa(\\rho_1;\\rho_2) processes are reversible if and only if both \\rho_i are at least \\kappa/2-4, which is the critical threshold at or below which such curves are boundary filling.\n  Our result supplies the missing ingredient needed to show that for all \\kappa \\in (4,8) the so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1498","kind":"arxiv","version":2},"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":"2026-05-18T01:19:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XW+A8ysYryA0xFqT+cidL0KQa4JJFMjXaQebNmQ/deX882P01Gjwq90xVpn5A+aRwrdhs5lO95DNJQoIyAaDBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:02:51.708552Z"},"content_sha256":"efc4ea9ce053ab1c16c5a3a105e9b10d8dc72be28d0052d23865fda2e6481217","schema_version":"1.0","event_id":"sha256:efc4ea9ce053ab1c16c5a3a105e9b10d8dc72be28d0052d23865fda2e6481217"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FCC4VXALQD5PMSQYYJB33UR2V7/bundle.json","state_url":"https://pith.science/pith/FCC4VXALQD5PMSQYYJB33UR2V7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FCC4VXALQD5PMSQYYJB33UR2V7/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":"2026-05-27T14:02:51Z","links":{"resolver":"https://pith.science/pith/FCC4VXALQD5PMSQYYJB33UR2V7","bundle":"https://pith.science/pith/FCC4VXALQD5PMSQYYJB33UR2V7/bundle.json","state":"https://pith.science/pith/FCC4VXALQD5PMSQYYJB33UR2V7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FCC4VXALQD5PMSQYYJB33UR2V7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FCC4VXALQD5PMSQYYJB33UR2V7","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":"bdb26a75a7a196fbb7ccf9e72a9d0150b8721bc119004e9db2ea6f3a177a51cb","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-06T20:56:04Z","title_canon_sha256":"154d52f9b439c24076f8fce57d5377a06f572b2921fe12ff3a1deaa853b88d64"},"schema_version":"1.0","source":{"id":"1201.1498","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1498","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1498v2","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1498","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"pith_short_12","alias_value":"FCC4VXALQD5P","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FCC4VXALQD5PMSQY","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FCC4VXAL","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:efc4ea9ce053ab1c16c5a3a105e9b10d8dc72be28d0052d23865fda2e6481217","target":"graph","created_at":"2026-05-18T01:19:55Z","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":"Suppose that D is a planar Jordan domain and x and y are distinct boundary points of D. Fix \\kappa \\in (4,8) and let \\eta\\ be an SLE_\\kappa process from x to y in D. We prove that the law of the time-reversal of \\eta is, up to reparameterization, an SLE_\\kappa process from y to x in D. More generally, we prove that SLE_\\kappa(\\rho_1;\\rho_2) processes are reversible if and only if both \\rho_i are at least \\kappa/2-4, which is the critical threshold at or below which such curves are boundary filling.\n  Our result supplies the missing ingredient needed to show that for all \\kappa \\in (4,8) the so","authors_text":"Jason Miller, Scott Sheffield","cross_cats":["math-ph","math.CV","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-06T20:56:04Z","title":"Imaginary geometry III: reversibility of SLE_\\kappa\\ for \\kappa \\in (4,8)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1498","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":"sha256:060fe8991ac83b2ded3939788ab095abb0af4a6c4e64cd61fb1e31d009dca8bd","target":"record","created_at":"2026-05-18T01:19:55Z","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":"bdb26a75a7a196fbb7ccf9e72a9d0150b8721bc119004e9db2ea6f3a177a51cb","cross_cats_sorted":["math-ph","math.CV","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-06T20:56:04Z","title_canon_sha256":"154d52f9b439c24076f8fce57d5377a06f572b2921fe12ff3a1deaa853b88d64"},"schema_version":"1.0","source":{"id":"1201.1498","kind":"arxiv","version":2}},"canonical_sha256":"2885cadc0b80faf64a18c243bdd23aafcab419ea01d4c9ff9d728a00b969216e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2885cadc0b80faf64a18c243bdd23aafcab419ea01d4c9ff9d728a00b969216e","first_computed_at":"2026-05-18T01:19:55.869598Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:55.869598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LZ3ZNYgUTdZq+oK4AKCQ8+wYXrNqGaEXKaVI+bYRR9ZHY779bpHargapPolw9dOPRg9HhoPBBwCJam1YUXzUBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:55.870252Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.1498","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:060fe8991ac83b2ded3939788ab095abb0af4a6c4e64cd61fb1e31d009dca8bd","sha256:efc4ea9ce053ab1c16c5a3a105e9b10d8dc72be28d0052d23865fda2e6481217"],"state_sha256":"6679d45b6c093384b57935c2224ad760ed4600d70cde7a68ec85fc73e4f2e586"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5oTessp/ATbHUEUHfAlqeahaP04HmWbTZUtCgK6eArqYgt7/u6G/zRlZiFgKVRYb8oEOmMLZDsXggO2tD6m6Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:02:51.711040Z","bundle_sha256":"6810677b431d07a3fc9ec64a63a62d9f4035cff044c09a26929deb92e5bf9cc2"}}