{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6LLAMYQHPDBZWTCDKAWGYIGCE2","short_pith_number":"pith:6LLAMYQH","canonical_record":{"source":{"id":"1611.10234","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-11-30T15:49:05Z","cross_cats_sorted":[],"title_canon_sha256":"445a23dd97dd193ff4cb704bc95217c01544292c0a90e4cfc1340a11b3f7e613","abstract_canon_sha256":"7d18b003660c0a9311217b55f9c23a7be826ac13e50cb31e7b7ac7d7ab3d5002"},"schema_version":"1.0"},"canonical_sha256":"f2d606620778c39b4c43502c6c20c2269beb0359076df2150f18e7852de0c0de","source":{"kind":"arxiv","id":"1611.10234","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.10234","created_at":"2026-07-05T10:31:36Z"},{"alias_kind":"arxiv_version","alias_value":"1611.10234v3","created_at":"2026-07-05T10:31:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.10234","created_at":"2026-07-05T10:31:36Z"},{"alias_kind":"pith_short_12","alias_value":"6LLAMYQHPDBZ","created_at":"2026-07-05T10:31:36Z"},{"alias_kind":"pith_short_16","alias_value":"6LLAMYQHPDBZWTCD","created_at":"2026-07-05T10:31:36Z"},{"alias_kind":"pith_short_8","alias_value":"6LLAMYQH","created_at":"2026-07-05T10:31:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6LLAMYQHPDBZWTCDKAWGYIGCE2","target":"record","payload":{"canonical_record":{"source":{"id":"1611.10234","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-11-30T15:49:05Z","cross_cats_sorted":[],"title_canon_sha256":"445a23dd97dd193ff4cb704bc95217c01544292c0a90e4cfc1340a11b3f7e613","abstract_canon_sha256":"7d18b003660c0a9311217b55f9c23a7be826ac13e50cb31e7b7ac7d7ab3d5002"},"schema_version":"1.0"},"canonical_sha256":"f2d606620778c39b4c43502c6c20c2269beb0359076df2150f18e7852de0c0de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:31:36.975769Z","signature_b64":"/nYtk0eT9VTJWkKlL8jwJWtZ9Gtv56X1HtdZ70ZLuMnyg0VEMmSpvykz76nxg3tflTNU6CNPqPlkTQSUeEobCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2d606620778c39b4c43502c6c20c2269beb0359076df2150f18e7852de0c0de","last_reissued_at":"2026-07-05T10:31:36.974947Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:31:36.974947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.10234","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":"2026-07-05T10:31:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W9aINbOCZjuzPEIDADnv5WpJuDAIZoNATqHkOcs+zwIMLze8Fdt74yk5jGFPDZ41yqdvj518Lz1lJV3V7PDeDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T11:29:50.528979Z"},"content_sha256":"6d0ada34066553640016147816b98dbb378db080d20adc6f44dc6a59eb821c3b","schema_version":"1.0","event_id":"sha256:6d0ada34066553640016147816b98dbb378db080d20adc6f44dc6a59eb821c3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6LLAMYQHPDBZWTCDKAWGYIGCE2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Slice starlike functions over quaternions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Guangbin Ren, Zhenghua Xu","submitted_at":"2016-11-30T15:49:05Z","abstract_excerpt":"In this paper, we initiate the study of the geometric function theory for slice starlike functions over quaternions and its subclasses. This allows us to answer negatively some questions about the Bieberbach conjecture, the growth, distortion, and covering theorems for slice regular functions. Precisely, we find that the Bieberbach conjecture holds true for slice starlike functions in contrast to the fact that the Bieberbach conjecture fails for biholomorphic starlike mappings in higher dimensions. We also establish some sharp versions of the growth, distortion, and covering theorems for quate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.10234","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1611.10234/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:31:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pLOvAyMGTLHB5Z2EFZFdldPZTaBe39L6vk0lxgC9IbEjrGCV4poS9p5OjpwbFVR4AMC/hd3QXtdLYvl2rBKyBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T11:29:50.529358Z"},"content_sha256":"2923780ecdcf6aca3f8a32733f96219a5a3c7b3cc8074276e56f8b527d1051d2","schema_version":"1.0","event_id":"sha256:2923780ecdcf6aca3f8a32733f96219a5a3c7b3cc8074276e56f8b527d1051d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6LLAMYQHPDBZWTCDKAWGYIGCE2/bundle.json","state_url":"https://pith.science/pith/6LLAMYQHPDBZWTCDKAWGYIGCE2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6LLAMYQHPDBZWTCDKAWGYIGCE2/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":"2026-07-06T11:29:50Z","links":{"resolver":"https://pith.science/pith/6LLAMYQHPDBZWTCDKAWGYIGCE2","bundle":"https://pith.science/pith/6LLAMYQHPDBZWTCDKAWGYIGCE2/bundle.json","state":"https://pith.science/pith/6LLAMYQHPDBZWTCDKAWGYIGCE2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6LLAMYQHPDBZWTCDKAWGYIGCE2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6LLAMYQHPDBZWTCDKAWGYIGCE2","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":"7d18b003660c0a9311217b55f9c23a7be826ac13e50cb31e7b7ac7d7ab3d5002","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-11-30T15:49:05Z","title_canon_sha256":"445a23dd97dd193ff4cb704bc95217c01544292c0a90e4cfc1340a11b3f7e613"},"schema_version":"1.0","source":{"id":"1611.10234","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.10234","created_at":"2026-07-05T10:31:36Z"},{"alias_kind":"arxiv_version","alias_value":"1611.10234v3","created_at":"2026-07-05T10:31:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.10234","created_at":"2026-07-05T10:31:36Z"},{"alias_kind":"pith_short_12","alias_value":"6LLAMYQHPDBZ","created_at":"2026-07-05T10:31:36Z"},{"alias_kind":"pith_short_16","alias_value":"6LLAMYQHPDBZWTCD","created_at":"2026-07-05T10:31:36Z"},{"alias_kind":"pith_short_8","alias_value":"6LLAMYQH","created_at":"2026-07-05T10:31:36Z"}],"graph_snapshots":[{"event_id":"sha256:2923780ecdcf6aca3f8a32733f96219a5a3c7b3cc8074276e56f8b527d1051d2","target":"graph","created_at":"2026-07-05T10:31:36Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1611.10234/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we initiate the study of the geometric function theory for slice starlike functions over quaternions and its subclasses. This allows us to answer negatively some questions about the Bieberbach conjecture, the growth, distortion, and covering theorems for slice regular functions. Precisely, we find that the Bieberbach conjecture holds true for slice starlike functions in contrast to the fact that the Bieberbach conjecture fails for biholomorphic starlike mappings in higher dimensions. We also establish some sharp versions of the growth, distortion, and covering theorems for quate","authors_text":"Guangbin Ren, Zhenghua Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-11-30T15:49:05Z","title":"Slice starlike functions over quaternions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.10234","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":"sha256:6d0ada34066553640016147816b98dbb378db080d20adc6f44dc6a59eb821c3b","target":"record","created_at":"2026-07-05T10:31:36Z","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":"7d18b003660c0a9311217b55f9c23a7be826ac13e50cb31e7b7ac7d7ab3d5002","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-11-30T15:49:05Z","title_canon_sha256":"445a23dd97dd193ff4cb704bc95217c01544292c0a90e4cfc1340a11b3f7e613"},"schema_version":"1.0","source":{"id":"1611.10234","kind":"arxiv","version":3}},"canonical_sha256":"f2d606620778c39b4c43502c6c20c2269beb0359076df2150f18e7852de0c0de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2d606620778c39b4c43502c6c20c2269beb0359076df2150f18e7852de0c0de","first_computed_at":"2026-07-05T10:31:36.974947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:31:36.974947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/nYtk0eT9VTJWkKlL8jwJWtZ9Gtv56X1HtdZ70ZLuMnyg0VEMmSpvykz76nxg3tflTNU6CNPqPlkTQSUeEobCA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:31:36.975769Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.10234","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d0ada34066553640016147816b98dbb378db080d20adc6f44dc6a59eb821c3b","sha256:2923780ecdcf6aca3f8a32733f96219a5a3c7b3cc8074276e56f8b527d1051d2"],"state_sha256":"0ee60b961d692ba5b4fc96632f16a40c46725c1f1a617587ff7b41500a77d4b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3d4juylJLAUbKErcR5n5b989eHlVl7EhE4CXccAFG04EyNPf8DZUwzw9OyI8sNp27EpFcoZa38aQjk+Y5SREBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T11:29:50.531258Z","bundle_sha256":"97e1ede3b6fcc946007774fb68bfcb46702f185291414de9a60d4de2caba9bf6"}}