{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SADEWZXB62UURU3JE2RMAZRLZS","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":"f03a354fd72b8267c87b19fc491ae13fc635b2028bb11ca615e46f6539a06c5c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-10T05:40:18Z","title_canon_sha256":"d3229f338c78508c37ba3c297eb3dceb7f2851063743a299385540274f7d5f28"},"schema_version":"1.0","source":{"id":"1502.02787","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02787","created_at":"2026-05-18T02:27:30Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02787v1","created_at":"2026-05-18T02:27:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02787","created_at":"2026-05-18T02:27:30Z"},{"alias_kind":"pith_short_12","alias_value":"SADEWZXB62UU","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"SADEWZXB62UURU3J","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"SADEWZXB","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:65c7c0ecc338729773a79ee1ef99c4479a8543554634c58a46faf9c5f793dc54","target":"graph","created_at":"2026-05-18T02:27:30Z","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":"This paper is concerned with the connection between G-Brownian Motion and analytic functions. We introduce the complex version of sublinear expectation, and then do the stochastic analysis in this framework. Furthermore, the conformal G-Brownian Motion is introduced together with a representation, and the corresponding conformal invariance is shown.","authors_text":"Huilin Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-10T05:40:18Z","title":"A Complex Version of G-Expectation and its Application to Conformal Martingale"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02787","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":"sha256:57d8c43a190c80ea636f57f7d76f7728d7f85466fcfe41adbd8984ad52b8b4e8","target":"record","created_at":"2026-05-18T02:27:30Z","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":"f03a354fd72b8267c87b19fc491ae13fc635b2028bb11ca615e46f6539a06c5c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-10T05:40:18Z","title_canon_sha256":"d3229f338c78508c37ba3c297eb3dceb7f2851063743a299385540274f7d5f28"},"schema_version":"1.0","source":{"id":"1502.02787","kind":"arxiv","version":1}},"canonical_sha256":"90064b66e1f6a948d36926a2c0662bccb471abecd2f9c692a6613aee9a1abf39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90064b66e1f6a948d36926a2c0662bccb471abecd2f9c692a6613aee9a1abf39","first_computed_at":"2026-05-18T02:27:30.956086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:30.956086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p/VyX6EtLRgZSRzqBeO0CCn0WJ3XOaApLTRvF8Ij/XWfFBcHrnmdBTx/DCCAaFHWVTHUUtSiDZzdWNKZ6FFpDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:30.956943Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.02787","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57d8c43a190c80ea636f57f7d76f7728d7f85466fcfe41adbd8984ad52b8b4e8","sha256:65c7c0ecc338729773a79ee1ef99c4479a8543554634c58a46faf9c5f793dc54"],"state_sha256":"b9d7274c61b3abfe8377669bd793239cb40b471c7b0f60a981b84c7ca2faf020"}