{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NUFKSQ25R5PNZIKORYGBKUIULZ","short_pith_number":"pith:NUFKSQ25","canonical_record":{"source":{"id":"1202.3063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-02-14T15:20:23Z","cross_cats_sorted":[],"title_canon_sha256":"41aee96ef785cf9e69242faecebc21c5b662e3a7015d4c1115287c87a358330d","abstract_canon_sha256":"8ac716fe1c3e5786f36f524247b8eb808404489dcccdbe1b17032d5a41f58467"},"schema_version":"1.0"},"canonical_sha256":"6d0aa9435d8f5edca14e8e0c1551145e52667a990a2ea2e33d20d2eb881051a0","source":{"kind":"arxiv","id":"1202.3063","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3063","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3063v1","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3063","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"pith_short_12","alias_value":"NUFKSQ25R5PN","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NUFKSQ25R5PNZIKO","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NUFKSQ25","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NUFKSQ25R5PNZIKORYGBKUIULZ","target":"record","payload":{"canonical_record":{"source":{"id":"1202.3063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-02-14T15:20:23Z","cross_cats_sorted":[],"title_canon_sha256":"41aee96ef785cf9e69242faecebc21c5b662e3a7015d4c1115287c87a358330d","abstract_canon_sha256":"8ac716fe1c3e5786f36f524247b8eb808404489dcccdbe1b17032d5a41f58467"},"schema_version":"1.0"},"canonical_sha256":"6d0aa9435d8f5edca14e8e0c1551145e52667a990a2ea2e33d20d2eb881051a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:24.192942Z","signature_b64":"kJKVlOPDegy8vhhcO1F877TZsCF8hpksMw0U2oFfTFLO10ebMK5hgnViECR2A51W90dE1MeNAzuLanKdd4kCCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d0aa9435d8f5edca14e8e0c1551145e52667a990a2ea2e33d20d2eb881051a0","last_reissued_at":"2026-05-18T04:02:24.192313Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:24.192313Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.3063","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:02:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qS5lxM6YU8/ghbzcjKTsSJUfRX7T3mrGOhs1x47AdM/hUQ3FamG3nRu08NUSq1IINFR/ZVDlEgPtpgg505I4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:58:00.906930Z"},"content_sha256":"ad9949be9de794df2ef0c24a92aaacfbd56c92523ea310bbc5d6eb38421c8621","schema_version":"1.0","event_id":"sha256:ad9949be9de794df2ef0c24a92aaacfbd56c92523ea310bbc5d6eb38421c8621"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NUFKSQ25R5PNZIKORYGBKUIULZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Covering results and perturbed Roper--Suffridge operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Marina Levenshtein, Mark Elin","submitted_at":"2012-02-14T15:20:23Z","abstract_excerpt":"This work is devoted to the advanced study of Roper--Suffridge type extension operators. For a given non-normalized spirallike function (with respect to an interior or boundary point) on the open unit disk of the complex plane, we construct perturbed extension operators in a certain class of Banach spaces and prove that these operators preserve the spirallikeness property. In addition, we present an extension operator for semigroup generators.\n  We use a new geometric approach based on the connection between spirallike mappings and one-parameter continuous semigroups. It turns out that the new"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3063","kind":"arxiv","version":1},"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":"2026-05-18T04:02:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5MzAUu+QZxF3nK0i5/52i6ypcJQYGcqkVrfPOKlgIeuGNEA0pTTnJBX3DNI4FNmrXSDtrPyYggGCJpm0+L3XBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:58:00.907669Z"},"content_sha256":"97396d2bbb68f53ba6c6cb71d489080754d8ff07a88d7ec4613f74b6f2091a63","schema_version":"1.0","event_id":"sha256:97396d2bbb68f53ba6c6cb71d489080754d8ff07a88d7ec4613f74b6f2091a63"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NUFKSQ25R5PNZIKORYGBKUIULZ/bundle.json","state_url":"https://pith.science/pith/NUFKSQ25R5PNZIKORYGBKUIULZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NUFKSQ25R5PNZIKORYGBKUIULZ/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":"2026-06-01T00:58:00Z","links":{"resolver":"https://pith.science/pith/NUFKSQ25R5PNZIKORYGBKUIULZ","bundle":"https://pith.science/pith/NUFKSQ25R5PNZIKORYGBKUIULZ/bundle.json","state":"https://pith.science/pith/NUFKSQ25R5PNZIKORYGBKUIULZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NUFKSQ25R5PNZIKORYGBKUIULZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NUFKSQ25R5PNZIKORYGBKUIULZ","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":"8ac716fe1c3e5786f36f524247b8eb808404489dcccdbe1b17032d5a41f58467","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-02-14T15:20:23Z","title_canon_sha256":"41aee96ef785cf9e69242faecebc21c5b662e3a7015d4c1115287c87a358330d"},"schema_version":"1.0","source":{"id":"1202.3063","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3063","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3063v1","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3063","created_at":"2026-05-18T04:02:24Z"},{"alias_kind":"pith_short_12","alias_value":"NUFKSQ25R5PN","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NUFKSQ25R5PNZIKO","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NUFKSQ25","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:97396d2bbb68f53ba6c6cb71d489080754d8ff07a88d7ec4613f74b6f2091a63","target":"graph","created_at":"2026-05-18T04:02:24Z","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 work is devoted to the advanced study of Roper--Suffridge type extension operators. For a given non-normalized spirallike function (with respect to an interior or boundary point) on the open unit disk of the complex plane, we construct perturbed extension operators in a certain class of Banach spaces and prove that these operators preserve the spirallikeness property. In addition, we present an extension operator for semigroup generators.\n  We use a new geometric approach based on the connection between spirallike mappings and one-parameter continuous semigroups. It turns out that the new","authors_text":"Marina Levenshtein, Mark Elin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-02-14T15:20:23Z","title":"Covering results and perturbed Roper--Suffridge operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3063","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:ad9949be9de794df2ef0c24a92aaacfbd56c92523ea310bbc5d6eb38421c8621","target":"record","created_at":"2026-05-18T04:02:24Z","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":"8ac716fe1c3e5786f36f524247b8eb808404489dcccdbe1b17032d5a41f58467","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-02-14T15:20:23Z","title_canon_sha256":"41aee96ef785cf9e69242faecebc21c5b662e3a7015d4c1115287c87a358330d"},"schema_version":"1.0","source":{"id":"1202.3063","kind":"arxiv","version":1}},"canonical_sha256":"6d0aa9435d8f5edca14e8e0c1551145e52667a990a2ea2e33d20d2eb881051a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d0aa9435d8f5edca14e8e0c1551145e52667a990a2ea2e33d20d2eb881051a0","first_computed_at":"2026-05-18T04:02:24.192313Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:24.192313Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kJKVlOPDegy8vhhcO1F877TZsCF8hpksMw0U2oFfTFLO10ebMK5hgnViECR2A51W90dE1MeNAzuLanKdd4kCCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:24.192942Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3063","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad9949be9de794df2ef0c24a92aaacfbd56c92523ea310bbc5d6eb38421c8621","sha256:97396d2bbb68f53ba6c6cb71d489080754d8ff07a88d7ec4613f74b6f2091a63"],"state_sha256":"bbdec45a009958f228fe41411bcb80d376fc8a71d4df1b4e80351e79978eca58"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kF2A22Cg3lDFtlEnrmH9Baac1NC8BqjTeylY+ySBPDcH6FwpY94t5fGzaC2LiI8zRaK2VJXYcK3zLeiOVFkoCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:58:00.911813Z","bundle_sha256":"be00546113baa5c4d6551cfb03c722ae63252f11f15837423e1b16952cdda40c"}}