{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:G2NFOGZISOGQPPN3JJLDJZX2WW","short_pith_number":"pith:G2NFOGZI","canonical_record":{"source":{"id":"1808.06994","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-08-21T16:15:03Z","cross_cats_sorted":[],"title_canon_sha256":"b42b6aa7aee206f10b27e7028cbb585466fcae6af73840ca1c41c106a834b446","abstract_canon_sha256":"5b8eba905c8d77661428b5432dc780c79cfdf55ade103f07dbcc04228721123c"},"schema_version":"1.0"},"canonical_sha256":"369a571b28938d07bdbb4a5634e6fab5898d7512dfb1a17aaf88d7338cb14348","source":{"kind":"arxiv","id":"1808.06994","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.06994","created_at":"2026-05-17T23:54:16Z"},{"alias_kind":"arxiv_version","alias_value":"1808.06994v3","created_at":"2026-05-17T23:54:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.06994","created_at":"2026-05-17T23:54:16Z"},{"alias_kind":"pith_short_12","alias_value":"G2NFOGZISOGQ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G2NFOGZISOGQPPN3","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G2NFOGZI","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:G2NFOGZISOGQPPN3JJLDJZX2WW","target":"record","payload":{"canonical_record":{"source":{"id":"1808.06994","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-08-21T16:15:03Z","cross_cats_sorted":[],"title_canon_sha256":"b42b6aa7aee206f10b27e7028cbb585466fcae6af73840ca1c41c106a834b446","abstract_canon_sha256":"5b8eba905c8d77661428b5432dc780c79cfdf55ade103f07dbcc04228721123c"},"schema_version":"1.0"},"canonical_sha256":"369a571b28938d07bdbb4a5634e6fab5898d7512dfb1a17aaf88d7338cb14348","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:16.208879Z","signature_b64":"wJLVkhv1Q9ziOXcFeMFvGmUZg5RhIP7lh8TqGo3766VDLxS07azDMpkA+30gCDcxTH0Q+FgJKmPMU3cwKjCqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"369a571b28938d07bdbb4a5634e6fab5898d7512dfb1a17aaf88d7338cb14348","last_reissued_at":"2026-05-17T23:54:16.208249Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:16.208249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.06994","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:54:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BS0LrgddTjcHbQo0WKbMGB1i1EEWvDlAbbj27gf4c0YxGu3YavkR/i0acX6A5WTZlkR/2hqK5uTCr478bTgzDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T18:29:54.080339Z"},"content_sha256":"cfc9bd6958737eb2012818f681cf321629fd3666490404fa053c71f3feeba5fe","schema_version":"1.0","event_id":"sha256:cfc9bd6958737eb2012818f681cf321629fd3666490404fa053c71f3feeba5fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:G2NFOGZISOGQPPN3JJLDJZX2WW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Riemann slice-domains over quaternions I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Guangbin Ren, Xinyuan Dou","submitted_at":"2018-08-21T16:15:03Z","abstract_excerpt":"We construct a counterexample to a well-known extension theorem for slice regular functions, which motivates us to develop a theory of Riemann slice-domains by introducing a new topology on quaternions. By some paths describing axial symmetry in Riemann slice-domains, we rectify the classical extension formula in the theory of slice regular functions and prove a representation formula over slice-domains of regularity. This proof involves an intertwining relation between imaginary units of quaternions and a fixed matrix corresponding to a complex structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06994","kind":"arxiv","version":3},"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":"2026-05-17T23:54:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zXOEDriM5WHyYnWuS2it94HyZfq/HENVvks7Ca7HRMFjJNhNqbvwScGygMnEnX2Sq68OtqqO/QQzjjyn7hOqCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T18:29:54.080677Z"},"content_sha256":"450164fc7395a46ba263a0d54b420672506675bd3a364082be98ab4179f0ac06","schema_version":"1.0","event_id":"sha256:450164fc7395a46ba263a0d54b420672506675bd3a364082be98ab4179f0ac06"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G2NFOGZISOGQPPN3JJLDJZX2WW/bundle.json","state_url":"https://pith.science/pith/G2NFOGZISOGQPPN3JJLDJZX2WW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G2NFOGZISOGQPPN3JJLDJZX2WW/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":"2026-07-04T18:29:54Z","links":{"resolver":"https://pith.science/pith/G2NFOGZISOGQPPN3JJLDJZX2WW","bundle":"https://pith.science/pith/G2NFOGZISOGQPPN3JJLDJZX2WW/bundle.json","state":"https://pith.science/pith/G2NFOGZISOGQPPN3JJLDJZX2WW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G2NFOGZISOGQPPN3JJLDJZX2WW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:G2NFOGZISOGQPPN3JJLDJZX2WW","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":"5b8eba905c8d77661428b5432dc780c79cfdf55ade103f07dbcc04228721123c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-08-21T16:15:03Z","title_canon_sha256":"b42b6aa7aee206f10b27e7028cbb585466fcae6af73840ca1c41c106a834b446"},"schema_version":"1.0","source":{"id":"1808.06994","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.06994","created_at":"2026-05-17T23:54:16Z"},{"alias_kind":"arxiv_version","alias_value":"1808.06994v3","created_at":"2026-05-17T23:54:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.06994","created_at":"2026-05-17T23:54:16Z"},{"alias_kind":"pith_short_12","alias_value":"G2NFOGZISOGQ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G2NFOGZISOGQPPN3","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G2NFOGZI","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:450164fc7395a46ba263a0d54b420672506675bd3a364082be98ab4179f0ac06","target":"graph","created_at":"2026-05-17T23:54:16Z","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 construct a counterexample to a well-known extension theorem for slice regular functions, which motivates us to develop a theory of Riemann slice-domains by introducing a new topology on quaternions. By some paths describing axial symmetry in Riemann slice-domains, we rectify the classical extension formula in the theory of slice regular functions and prove a representation formula over slice-domains of regularity. This proof involves an intertwining relation between imaginary units of quaternions and a fixed matrix corresponding to a complex structure.","authors_text":"Guangbin Ren, Xinyuan Dou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-08-21T16:15:03Z","title":"Riemann slice-domains over quaternions I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06994","kind":"arxiv","version":3},"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:cfc9bd6958737eb2012818f681cf321629fd3666490404fa053c71f3feeba5fe","target":"record","created_at":"2026-05-17T23:54:16Z","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":"5b8eba905c8d77661428b5432dc780c79cfdf55ade103f07dbcc04228721123c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-08-21T16:15:03Z","title_canon_sha256":"b42b6aa7aee206f10b27e7028cbb585466fcae6af73840ca1c41c106a834b446"},"schema_version":"1.0","source":{"id":"1808.06994","kind":"arxiv","version":3}},"canonical_sha256":"369a571b28938d07bdbb4a5634e6fab5898d7512dfb1a17aaf88d7338cb14348","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"369a571b28938d07bdbb4a5634e6fab5898d7512dfb1a17aaf88d7338cb14348","first_computed_at":"2026-05-17T23:54:16.208249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:16.208249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wJLVkhv1Q9ziOXcFeMFvGmUZg5RhIP7lh8TqGo3766VDLxS07azDMpkA+30gCDcxTH0Q+FgJKmPMU3cwKjCqDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:16.208879Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.06994","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfc9bd6958737eb2012818f681cf321629fd3666490404fa053c71f3feeba5fe","sha256:450164fc7395a46ba263a0d54b420672506675bd3a364082be98ab4179f0ac06"],"state_sha256":"962fc830f418894acbbae9948158940bda8af16ace6bd7566724387fe1f6145c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/TgpLN1jqG469ffOj9ii6WnkT0ruMw1VJhxsdnE2OIbqZacxURQTf4uYUuqJywBwlIXN3BtbN+pmOy/GmkABDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T18:29:54.082668Z","bundle_sha256":"5802713b32067da3f779caaacd94dfbfa1179807a1f3b8774deafc28d6274d41"}}