{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XLRIEJ2QMVWZYE4ZHNVEW7U26M","short_pith_number":"pith:XLRIEJ2Q","canonical_record":{"source":{"id":"1502.02368","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-02-09T05:26:50Z","cross_cats_sorted":[],"title_canon_sha256":"47740b3905bf66cb4e5ea47cd7ecdb60d2fa6236d1db4b5310cf3e776b4e1fe5","abstract_canon_sha256":"8e6fa25256e6bb35e6f8129392eb127bf898539f12442c0dfceba2d2cb70d5f3"},"schema_version":"1.0"},"canonical_sha256":"bae2822750656d9c13993b6a4b7e9af32abc158aa0b3437ad7fc410afb6eaa10","source":{"kind":"arxiv","id":"1502.02368","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02368","created_at":"2026-05-18T01:18:52Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02368v3","created_at":"2026-05-18T01:18:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02368","created_at":"2026-05-18T01:18:52Z"},{"alias_kind":"pith_short_12","alias_value":"XLRIEJ2QMVWZ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XLRIEJ2QMVWZYE4Z","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XLRIEJ2Q","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XLRIEJ2QMVWZYE4ZHNVEW7U26M","target":"record","payload":{"canonical_record":{"source":{"id":"1502.02368","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-02-09T05:26:50Z","cross_cats_sorted":[],"title_canon_sha256":"47740b3905bf66cb4e5ea47cd7ecdb60d2fa6236d1db4b5310cf3e776b4e1fe5","abstract_canon_sha256":"8e6fa25256e6bb35e6f8129392eb127bf898539f12442c0dfceba2d2cb70d5f3"},"schema_version":"1.0"},"canonical_sha256":"bae2822750656d9c13993b6a4b7e9af32abc158aa0b3437ad7fc410afb6eaa10","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:52.773898Z","signature_b64":"g4nBvNNS6gXIbbJGx8u/Ko4TeRtvGhHzLjoks4tWh/eAJRxM5LboF0u+4AdxPaGJyuCRcEboyxpiIFKiElDdBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bae2822750656d9c13993b6a4b7e9af32abc158aa0b3437ad7fc410afb6eaa10","last_reissued_at":"2026-05-18T01:18:52.773416Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:52.773416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.02368","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":"2026-05-18T01:18:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l9XzwC29x5/ZAHm0B/Pb+0/NtF3F0ut7dpceBiVKWeXVnwM8PeWRaFOVY035gSrY3BcAkXUavkGUFeiFDRXZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T19:53:37.910812Z"},"content_sha256":"12564c3ece6f2f0a700389b7fee0466d2bb138e1ddf3878a52c0e1de45545580","schema_version":"1.0","event_id":"sha256:12564c3ece6f2f0a700389b7fee0466d2bb138e1ddf3878a52c0e1de45545580"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XLRIEJ2QMVWZYE4ZHNVEW7U26M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Julia theory for slice regular functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Guangbin Ren, Xieping Wang","submitted_at":"2015-02-09T05:26:50Z","abstract_excerpt":"Slice regular functions have been extensively studied over the past decade, but much less is known about their boundary behavior. In this paper, we initiate the study of Julia theory for slice regular functions. More specifically, we establish the quaternionic versions of the Julia lemma, the Julia-Carath\\'{e}odory theorem, the boundary Schwarz lemma, and the Burns-Krantz rigidity theorem for slice regular self-mappings of the open unit ball $\\mathbb B$ and of the right half-space $\\mathbb H^+$. Our quaternionic boundary Schwarz lemma involves a Lie bracket reflecting the non-commutativity of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02368","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":"2026-05-18T01:18:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QNImU+Udfwee4b6eL4F05G9EQrbccT5OjWL0IUllluFIIzcniVymzPW6SYbZDZb38UsnpKfpP08L1gQVt/5jAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T19:53:37.911160Z"},"content_sha256":"2ad3cf2db6bd132dc60cd31daaf2f2c22add42ced5198704bd131b3d92c10fa3","schema_version":"1.0","event_id":"sha256:2ad3cf2db6bd132dc60cd31daaf2f2c22add42ced5198704bd131b3d92c10fa3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XLRIEJ2QMVWZYE4ZHNVEW7U26M/bundle.json","state_url":"https://pith.science/pith/XLRIEJ2QMVWZYE4ZHNVEW7U26M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XLRIEJ2QMVWZYE4ZHNVEW7U26M/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":"2026-07-04T19:53:37Z","links":{"resolver":"https://pith.science/pith/XLRIEJ2QMVWZYE4ZHNVEW7U26M","bundle":"https://pith.science/pith/XLRIEJ2QMVWZYE4ZHNVEW7U26M/bundle.json","state":"https://pith.science/pith/XLRIEJ2QMVWZYE4ZHNVEW7U26M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XLRIEJ2QMVWZYE4ZHNVEW7U26M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XLRIEJ2QMVWZYE4ZHNVEW7U26M","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":"8e6fa25256e6bb35e6f8129392eb127bf898539f12442c0dfceba2d2cb70d5f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-02-09T05:26:50Z","title_canon_sha256":"47740b3905bf66cb4e5ea47cd7ecdb60d2fa6236d1db4b5310cf3e776b4e1fe5"},"schema_version":"1.0","source":{"id":"1502.02368","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02368","created_at":"2026-05-18T01:18:52Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02368v3","created_at":"2026-05-18T01:18:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02368","created_at":"2026-05-18T01:18:52Z"},{"alias_kind":"pith_short_12","alias_value":"XLRIEJ2QMVWZ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XLRIEJ2QMVWZYE4Z","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XLRIEJ2Q","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:2ad3cf2db6bd132dc60cd31daaf2f2c22add42ced5198704bd131b3d92c10fa3","target":"graph","created_at":"2026-05-18T01:18:52Z","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":"Slice regular functions have been extensively studied over the past decade, but much less is known about their boundary behavior. In this paper, we initiate the study of Julia theory for slice regular functions. More specifically, we establish the quaternionic versions of the Julia lemma, the Julia-Carath\\'{e}odory theorem, the boundary Schwarz lemma, and the Burns-Krantz rigidity theorem for slice regular self-mappings of the open unit ball $\\mathbb B$ and of the right half-space $\\mathbb H^+$. Our quaternionic boundary Schwarz lemma involves a Lie bracket reflecting the non-commutativity of ","authors_text":"Guangbin Ren, Xieping Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-02-09T05:26:50Z","title":"Julia theory for slice regular functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02368","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":"sha256:12564c3ece6f2f0a700389b7fee0466d2bb138e1ddf3878a52c0e1de45545580","target":"record","created_at":"2026-05-18T01:18:52Z","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":"8e6fa25256e6bb35e6f8129392eb127bf898539f12442c0dfceba2d2cb70d5f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-02-09T05:26:50Z","title_canon_sha256":"47740b3905bf66cb4e5ea47cd7ecdb60d2fa6236d1db4b5310cf3e776b4e1fe5"},"schema_version":"1.0","source":{"id":"1502.02368","kind":"arxiv","version":3}},"canonical_sha256":"bae2822750656d9c13993b6a4b7e9af32abc158aa0b3437ad7fc410afb6eaa10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bae2822750656d9c13993b6a4b7e9af32abc158aa0b3437ad7fc410afb6eaa10","first_computed_at":"2026-05-18T01:18:52.773416Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:52.773416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g4nBvNNS6gXIbbJGx8u/Ko4TeRtvGhHzLjoks4tWh/eAJRxM5LboF0u+4AdxPaGJyuCRcEboyxpiIFKiElDdBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:52.773898Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.02368","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12564c3ece6f2f0a700389b7fee0466d2bb138e1ddf3878a52c0e1de45545580","sha256:2ad3cf2db6bd132dc60cd31daaf2f2c22add42ced5198704bd131b3d92c10fa3"],"state_sha256":"b7d66e5fcadb5bd1e33687efbfb642e340690c1d19b9a9397b4f93af202ffa30"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IM7s29G9DHRK2BzCOswLHIlphmJsegiCNiDEE4QYe23a0Sx/+6Z60wGZFLP24cxE1plsF4LT8SVgVI7MxAZkAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T19:53:37.913095Z","bundle_sha256":"0385284abb5bda632a5e794f62357b1f71fbcb6b024a87a391e7a5b6244c110a"}}