{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:WTLEZH2UUPQROQUHQ3SB4SH7SV","short_pith_number":"pith:WTLEZH2U","canonical_record":{"source":{"id":"1012.2620","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-13T03:02:35Z","cross_cats_sorted":["math.CA","math.CV"],"title_canon_sha256":"3985f60232e09c5870931c1b61739b38b822409f75ebd3d6aeccccae0def9ef2","abstract_canon_sha256":"ff1d1bec02cbd268fe9372093b482220201d6431878a08d9d591efbd718b69da"},"schema_version":"1.0"},"canonical_sha256":"b4d64c9f54a3e117428786e41e48ff957794c3192b60f6b0cf289b90c3c87d24","source":{"kind":"arxiv","id":"1012.2620","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2620","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2620v2","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2620","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"pith_short_12","alias_value":"WTLEZH2UUPQR","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"WTLEZH2UUPQROQUH","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"WTLEZH2U","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:WTLEZH2UUPQROQUHQ3SB4SH7SV","target":"record","payload":{"canonical_record":{"source":{"id":"1012.2620","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-13T03:02:35Z","cross_cats_sorted":["math.CA","math.CV"],"title_canon_sha256":"3985f60232e09c5870931c1b61739b38b822409f75ebd3d6aeccccae0def9ef2","abstract_canon_sha256":"ff1d1bec02cbd268fe9372093b482220201d6431878a08d9d591efbd718b69da"},"schema_version":"1.0"},"canonical_sha256":"b4d64c9f54a3e117428786e41e48ff957794c3192b60f6b0cf289b90c3c87d24","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:03.663798Z","signature_b64":"fQZOX3iAl656zjCym59QE/HVhHBrEwuEAQqDjw8Um7cNpVVnLY/NPbVOGe/9o7WqZUIM+1BMOMZj/DmyWYN9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4d64c9f54a3e117428786e41e48ff957794c3192b60f6b0cf289b90c3c87d24","last_reissued_at":"2026-05-18T04:30:03.663379Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:03.663379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.2620","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":"2026-05-18T04:30:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aj4ciEOZudY+GD98Q+1EvmG5+UbplgXf6LYS8jqzQL9Y8YMeqCAuNFBDuF/rwVcj2sMOsDXCQdURC/+jttUUAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:04:17.296695Z"},"content_sha256":"f322ace5d6f307a8be02dbf447cecb96dd22b9a6e9cba41136b327cadb5894f9","schema_version":"1.0","event_id":"sha256:f322ace5d6f307a8be02dbf447cecb96dd22b9a6e9cba41136b327cadb5894f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:WTLEZH2UUPQROQUHQ3SB4SH7SV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Twistor theory and the harmonic hull","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV"],"primary_cat":"math.DG","authors_text":"Feng Xu, Michael Eastwood","submitted_at":"2010-12-13T03:02:35Z","abstract_excerpt":"We use twistor theory to identify the harmonic hull of an arbitrary connected open subset U of R^{2m} for m at least 2. It is the natural domain of analytic continuation in C^{2m} for harmonic functions on U."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2620","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":"2026-05-18T04:30:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eyXGtmBGJbcgOqL0Z/YeEMOKNfPLV7HgOVKRCBLL3Hxr/kQ03g2ZAirllIdBVtj+fNBDfHe1qAf3qusckvb5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:04:17.297399Z"},"content_sha256":"c70131f906ac68d2fe81245d638f85b5d32c9ea4af1dfd2780a9eb6921a5846b","schema_version":"1.0","event_id":"sha256:c70131f906ac68d2fe81245d638f85b5d32c9ea4af1dfd2780a9eb6921a5846b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WTLEZH2UUPQROQUHQ3SB4SH7SV/bundle.json","state_url":"https://pith.science/pith/WTLEZH2UUPQROQUHQ3SB4SH7SV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WTLEZH2UUPQROQUHQ3SB4SH7SV/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":"2026-06-11T00:04:17Z","links":{"resolver":"https://pith.science/pith/WTLEZH2UUPQROQUHQ3SB4SH7SV","bundle":"https://pith.science/pith/WTLEZH2UUPQROQUHQ3SB4SH7SV/bundle.json","state":"https://pith.science/pith/WTLEZH2UUPQROQUHQ3SB4SH7SV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WTLEZH2UUPQROQUHQ3SB4SH7SV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:WTLEZH2UUPQROQUHQ3SB4SH7SV","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":"ff1d1bec02cbd268fe9372093b482220201d6431878a08d9d591efbd718b69da","cross_cats_sorted":["math.CA","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-13T03:02:35Z","title_canon_sha256":"3985f60232e09c5870931c1b61739b38b822409f75ebd3d6aeccccae0def9ef2"},"schema_version":"1.0","source":{"id":"1012.2620","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2620","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2620v2","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2620","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"pith_short_12","alias_value":"WTLEZH2UUPQR","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"WTLEZH2UUPQROQUH","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"WTLEZH2U","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:c70131f906ac68d2fe81245d638f85b5d32c9ea4af1dfd2780a9eb6921a5846b","target":"graph","created_at":"2026-05-18T04:30:03Z","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 use twistor theory to identify the harmonic hull of an arbitrary connected open subset U of R^{2m} for m at least 2. It is the natural domain of analytic continuation in C^{2m} for harmonic functions on U.","authors_text":"Feng Xu, Michael Eastwood","cross_cats":["math.CA","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-13T03:02:35Z","title":"Twistor theory and the harmonic hull"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2620","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:f322ace5d6f307a8be02dbf447cecb96dd22b9a6e9cba41136b327cadb5894f9","target":"record","created_at":"2026-05-18T04:30:03Z","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":"ff1d1bec02cbd268fe9372093b482220201d6431878a08d9d591efbd718b69da","cross_cats_sorted":["math.CA","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-12-13T03:02:35Z","title_canon_sha256":"3985f60232e09c5870931c1b61739b38b822409f75ebd3d6aeccccae0def9ef2"},"schema_version":"1.0","source":{"id":"1012.2620","kind":"arxiv","version":2}},"canonical_sha256":"b4d64c9f54a3e117428786e41e48ff957794c3192b60f6b0cf289b90c3c87d24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4d64c9f54a3e117428786e41e48ff957794c3192b60f6b0cf289b90c3c87d24","first_computed_at":"2026-05-18T04:30:03.663379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:03.663379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fQZOX3iAl656zjCym59QE/HVhHBrEwuEAQqDjw8Um7cNpVVnLY/NPbVOGe/9o7WqZUIM+1BMOMZj/DmyWYN9Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:03.663798Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.2620","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f322ace5d6f307a8be02dbf447cecb96dd22b9a6e9cba41136b327cadb5894f9","sha256:c70131f906ac68d2fe81245d638f85b5d32c9ea4af1dfd2780a9eb6921a5846b"],"state_sha256":"1a98504ee31a83c19dbac61dd14e9db9fda764d0c7a7c82b2b530043a1146931"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AJ3pIBSL9gDWqgZ28PMS7GDoxSxi/J4vR/U7d5QfEM/NmYxwvh5dnrqMgp+Zq+axVPjebM/FzAA2otAVpvfzBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T00:04:17.300106Z","bundle_sha256":"52e8d5c48f32a152e9f300b07d337129ea68e0c1f420cfb8f1f1a05e7e5f5107"}}