{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:YB26T76IVDPHGCL7FB4KVSQAVC","short_pith_number":"pith:YB26T76I","canonical_record":{"source":{"id":"1012.3113","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-14T18:07:54Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"4dffeed24a6bc12d770357316c01a2bd47e573cb3a221d9dfa15dba878ef9894","abstract_canon_sha256":"7e47f3c98e1534ff4fc721f24149b6e8a9454994050c08c2db0fef11e0251857"},"schema_version":"1.0"},"canonical_sha256":"c075e9ffc8a8de73097f2878aaca00a8836c1549daac64366fea64f392395f27","source":{"kind":"arxiv","id":"1012.3113","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3113","created_at":"2026-05-18T02:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3113v2","created_at":"2026-05-18T02:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3113","created_at":"2026-05-18T02:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"YB26T76IVDPH","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YB26T76IVDPHGCL7","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YB26T76I","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:YB26T76IVDPHGCL7FB4KVSQAVC","target":"record","payload":{"canonical_record":{"source":{"id":"1012.3113","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-14T18:07:54Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"4dffeed24a6bc12d770357316c01a2bd47e573cb3a221d9dfa15dba878ef9894","abstract_canon_sha256":"7e47f3c98e1534ff4fc721f24149b6e8a9454994050c08c2db0fef11e0251857"},"schema_version":"1.0"},"canonical_sha256":"c075e9ffc8a8de73097f2878aaca00a8836c1549daac64366fea64f392395f27","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:24.843050Z","signature_b64":"OoLTtgUFLDsW7jHfLHV9ctfT8Fwf3cBWsqDZwpzCP+uzzADs7ltKnYoJJLAOoBjRbtKaiER3fIPpPf9FgoLwDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c075e9ffc8a8de73097f2878aaca00a8836c1549daac64366fea64f392395f27","last_reissued_at":"2026-05-18T02:04:24.842469Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:24.842469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.3113","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":"2026-05-18T02:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j6pZJHWQwiS0ijnTO8gtBDc9ASWTqDgLzQpabpbkNnbOC+jbxIfuzT4NUmtXsTn3QeNG5bqxdXK9dz8xhNA2AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:49:17.958726Z"},"content_sha256":"99d26c236fb98fe43ae9fcb342726b5e44d415da8017a32dd205d4bacfec745d","schema_version":"1.0","event_id":"sha256:99d26c236fb98fe43ae9fcb342726b5e44d415da8017a32dd205d4bacfec745d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:YB26T76IVDPHGCL7FB4KVSQAVC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On SLE martingales in boundary WZW models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Andrei Bytsko, Anton Alekseev, Konstantin Izyurov","submitted_at":"2010-12-14T18:07:54Z","abstract_excerpt":"We consider the boundary WZW model on a half-plane with a cut growing according to the Schramm-Loewner stochastic evolution and the boundary fields inserted at the tip of the cut and at infinity. We study necessary and sufficient conditions for boundary correlation functions to be SLE martingales. Necessary conditions come from the requirement for the boundary field at the tip of the cut to have a depth two null vector. Sufficient conditions are established using Knizhnik-Zamolodchikov equations for boundary correlators. Combining these two approaches, we show that in the case of G=SU(2) the b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3113","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":"2026-05-18T02:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z9hG1fFkOHGwMhWtgm6PhOmvUQKT3KrLRLLCW71h1Z3CL9ghGtxiYdvzB+E7wM5CdzK8g3s/DL4Dv95K/Z66Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:49:17.959363Z"},"content_sha256":"a04573a0b9ddc8335fb8b98ff99828175dff4f5e2dd222162a9c9f2821e27b91","schema_version":"1.0","event_id":"sha256:a04573a0b9ddc8335fb8b98ff99828175dff4f5e2dd222162a9c9f2821e27b91"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YB26T76IVDPHGCL7FB4KVSQAVC/bundle.json","state_url":"https://pith.science/pith/YB26T76IVDPHGCL7FB4KVSQAVC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YB26T76IVDPHGCL7FB4KVSQAVC/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":"2026-06-07T09:49:17Z","links":{"resolver":"https://pith.science/pith/YB26T76IVDPHGCL7FB4KVSQAVC","bundle":"https://pith.science/pith/YB26T76IVDPHGCL7FB4KVSQAVC/bundle.json","state":"https://pith.science/pith/YB26T76IVDPHGCL7FB4KVSQAVC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YB26T76IVDPHGCL7FB4KVSQAVC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:YB26T76IVDPHGCL7FB4KVSQAVC","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":"7e47f3c98e1534ff4fc721f24149b6e8a9454994050c08c2db0fef11e0251857","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-14T18:07:54Z","title_canon_sha256":"4dffeed24a6bc12d770357316c01a2bd47e573cb3a221d9dfa15dba878ef9894"},"schema_version":"1.0","source":{"id":"1012.3113","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3113","created_at":"2026-05-18T02:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3113v2","created_at":"2026-05-18T02:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3113","created_at":"2026-05-18T02:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"YB26T76IVDPH","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YB26T76IVDPHGCL7","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YB26T76I","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:a04573a0b9ddc8335fb8b98ff99828175dff4f5e2dd222162a9c9f2821e27b91","target":"graph","created_at":"2026-05-18T02:04:24Z","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 consider the boundary WZW model on a half-plane with a cut growing according to the Schramm-Loewner stochastic evolution and the boundary fields inserted at the tip of the cut and at infinity. We study necessary and sufficient conditions for boundary correlation functions to be SLE martingales. Necessary conditions come from the requirement for the boundary field at the tip of the cut to have a depth two null vector. Sufficient conditions are established using Knizhnik-Zamolodchikov equations for boundary correlators. Combining these two approaches, we show that in the case of G=SU(2) the b","authors_text":"Andrei Bytsko, Anton Alekseev, Konstantin Izyurov","cross_cats":["hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-14T18:07:54Z","title":"On SLE martingales in boundary WZW models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3113","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":"sha256:99d26c236fb98fe43ae9fcb342726b5e44d415da8017a32dd205d4bacfec745d","target":"record","created_at":"2026-05-18T02:04:24Z","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":"7e47f3c98e1534ff4fc721f24149b6e8a9454994050c08c2db0fef11e0251857","cross_cats_sorted":["hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-14T18:07:54Z","title_canon_sha256":"4dffeed24a6bc12d770357316c01a2bd47e573cb3a221d9dfa15dba878ef9894"},"schema_version":"1.0","source":{"id":"1012.3113","kind":"arxiv","version":2}},"canonical_sha256":"c075e9ffc8a8de73097f2878aaca00a8836c1549daac64366fea64f392395f27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c075e9ffc8a8de73097f2878aaca00a8836c1549daac64366fea64f392395f27","first_computed_at":"2026-05-18T02:04:24.842469Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:24.842469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OoLTtgUFLDsW7jHfLHV9ctfT8Fwf3cBWsqDZwpzCP+uzzADs7ltKnYoJJLAOoBjRbtKaiER3fIPpPf9FgoLwDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:24.843050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.3113","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99d26c236fb98fe43ae9fcb342726b5e44d415da8017a32dd205d4bacfec745d","sha256:a04573a0b9ddc8335fb8b98ff99828175dff4f5e2dd222162a9c9f2821e27b91"],"state_sha256":"49f43e093734f2cf40328bd00dd8e963e5d9bccd6af342956a5429f8410ab1ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"18x4Rq5EFFyM7tXdbtGbZ33+a1V2FTZ5z/aaHVuos5UiFZ7QR6RdG0JzLZxG8jcRIGziHUnQLJ5jeX4/5PUAAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T09:49:17.962050Z","bundle_sha256":"7d47574802586fd35cc57de83e6eaa3ff357926a67b57827564961ed9d874973"}}