{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5NR4UNGTXU2XS4ZXXCNGGLHWMA","short_pith_number":"pith:5NR4UNGT","canonical_record":{"source":{"id":"1101.3832","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-01-20T07:15:01Z","cross_cats_sorted":[],"title_canon_sha256":"4c4d2637451dc19434a517709b06c4a7a17fd5883297848251e2464e76b96aba","abstract_canon_sha256":"4557907d5de7579bcad752dd5453762d6900b3fe3bbf18eeed5b31e89d1fd848"},"schema_version":"1.0"},"canonical_sha256":"eb63ca34d3bd35797337b89a632cf66027d0bb74d31e9888cc825ae537b8fd7f","source":{"kind":"arxiv","id":"1101.3832","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3832","created_at":"2026-05-18T04:31:21Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3832v1","created_at":"2026-05-18T04:31:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3832","created_at":"2026-05-18T04:31:21Z"},{"alias_kind":"pith_short_12","alias_value":"5NR4UNGTXU2X","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5NR4UNGTXU2XS4ZX","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5NR4UNGT","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5NR4UNGTXU2XS4ZXXCNGGLHWMA","target":"record","payload":{"canonical_record":{"source":{"id":"1101.3832","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-01-20T07:15:01Z","cross_cats_sorted":[],"title_canon_sha256":"4c4d2637451dc19434a517709b06c4a7a17fd5883297848251e2464e76b96aba","abstract_canon_sha256":"4557907d5de7579bcad752dd5453762d6900b3fe3bbf18eeed5b31e89d1fd848"},"schema_version":"1.0"},"canonical_sha256":"eb63ca34d3bd35797337b89a632cf66027d0bb74d31e9888cc825ae537b8fd7f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:21.271257Z","signature_b64":"lFxyP77fjii/fOqqQD5Vh6Mx5DzaZm/qaZMqrH+4fnfZWFRO6C4XhxYOff5Yjq1FPN3Pm4KyCDIR98HRPwjnCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb63ca34d3bd35797337b89a632cf66027d0bb74d31e9888cc825ae537b8fd7f","last_reissued_at":"2026-05-18T04:31:21.270558Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:21.270558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.3832","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":"2026-05-18T04:31:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K35u6ql/umh/gxu5bWhJfHn7I3cuG0kYLcEjVlW4YSEdAqcMz/53ElWzcGT0QtVqcCy40MorV3ELkJfZ0MhbBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:53:28.016434Z"},"content_sha256":"0e3edc84b6d385b817bc749f9b9ab3f2226b427b198e57e6bbf0bcb31bcc6936","schema_version":"1.0","event_id":"sha256:0e3edc84b6d385b817bc749f9b9ab3f2226b427b198e57e6bbf0bcb31bcc6936"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5NR4UNGTXU2XS4ZXXCNGGLHWMA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On power deformations of univalent functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Toshiyuki Sugawa, Yong Chan Kim","submitted_at":"2011-01-20T07:15:01Z","abstract_excerpt":"For an analytic function $f(z)$ on the unit disk $|z|<1$ with $f(0)=f'(0)-1=0$ and $f(z)\\ne0, 0<|z|<1,$ we consider the power deformation $f_c(z)=z(f(z)/z)^c$ for a complex number $c.$ We determine those values $c$ for which the operator $f\\mapsto f_c$ maps a specified class of univalent functions into the class of univalent functions. A little surprisingly, we will see that the set is described by the variability region of the quantity $zf'(z)/f(z),~|z|<1,$ for the class in most cases which we consider in the present paper. As an unexpected by-product, we show boundedness of strongly spiralli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3832","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":"2026-05-18T04:31:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yT5LgjMVbx8rzc4BydZ3705LVT/Tc4knhOy5w/bWV57zV6R6bc5Lr1awziLmjiSrBbHXOB5cH8JSHvFmGah3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:53:28.016778Z"},"content_sha256":"afaa1fefd123e68c49a732770a4970896305047fee84c7db21a22a9a3d079830","schema_version":"1.0","event_id":"sha256:afaa1fefd123e68c49a732770a4970896305047fee84c7db21a22a9a3d079830"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5NR4UNGTXU2XS4ZXXCNGGLHWMA/bundle.json","state_url":"https://pith.science/pith/5NR4UNGTXU2XS4ZXXCNGGLHWMA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5NR4UNGTXU2XS4ZXXCNGGLHWMA/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":"2026-06-23T00:53:28Z","links":{"resolver":"https://pith.science/pith/5NR4UNGTXU2XS4ZXXCNGGLHWMA","bundle":"https://pith.science/pith/5NR4UNGTXU2XS4ZXXCNGGLHWMA/bundle.json","state":"https://pith.science/pith/5NR4UNGTXU2XS4ZXXCNGGLHWMA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5NR4UNGTXU2XS4ZXXCNGGLHWMA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5NR4UNGTXU2XS4ZXXCNGGLHWMA","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":"4557907d5de7579bcad752dd5453762d6900b3fe3bbf18eeed5b31e89d1fd848","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-01-20T07:15:01Z","title_canon_sha256":"4c4d2637451dc19434a517709b06c4a7a17fd5883297848251e2464e76b96aba"},"schema_version":"1.0","source":{"id":"1101.3832","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3832","created_at":"2026-05-18T04:31:21Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3832v1","created_at":"2026-05-18T04:31:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3832","created_at":"2026-05-18T04:31:21Z"},{"alias_kind":"pith_short_12","alias_value":"5NR4UNGTXU2X","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5NR4UNGTXU2XS4ZX","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5NR4UNGT","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:afaa1fefd123e68c49a732770a4970896305047fee84c7db21a22a9a3d079830","target":"graph","created_at":"2026-05-18T04:31:21Z","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":"For an analytic function $f(z)$ on the unit disk $|z|<1$ with $f(0)=f'(0)-1=0$ and $f(z)\\ne0, 0<|z|<1,$ we consider the power deformation $f_c(z)=z(f(z)/z)^c$ for a complex number $c.$ We determine those values $c$ for which the operator $f\\mapsto f_c$ maps a specified class of univalent functions into the class of univalent functions. A little surprisingly, we will see that the set is described by the variability region of the quantity $zf'(z)/f(z),~|z|<1,$ for the class in most cases which we consider in the present paper. As an unexpected by-product, we show boundedness of strongly spiralli","authors_text":"Toshiyuki Sugawa, Yong Chan Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-01-20T07:15:01Z","title":"On power deformations of univalent functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3832","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":"sha256:0e3edc84b6d385b817bc749f9b9ab3f2226b427b198e57e6bbf0bcb31bcc6936","target":"record","created_at":"2026-05-18T04:31:21Z","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":"4557907d5de7579bcad752dd5453762d6900b3fe3bbf18eeed5b31e89d1fd848","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-01-20T07:15:01Z","title_canon_sha256":"4c4d2637451dc19434a517709b06c4a7a17fd5883297848251e2464e76b96aba"},"schema_version":"1.0","source":{"id":"1101.3832","kind":"arxiv","version":1}},"canonical_sha256":"eb63ca34d3bd35797337b89a632cf66027d0bb74d31e9888cc825ae537b8fd7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb63ca34d3bd35797337b89a632cf66027d0bb74d31e9888cc825ae537b8fd7f","first_computed_at":"2026-05-18T04:31:21.270558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:21.270558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lFxyP77fjii/fOqqQD5Vh6Mx5DzaZm/qaZMqrH+4fnfZWFRO6C4XhxYOff5Yjq1FPN3Pm4KyCDIR98HRPwjnCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:21.271257Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.3832","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e3edc84b6d385b817bc749f9b9ab3f2226b427b198e57e6bbf0bcb31bcc6936","sha256:afaa1fefd123e68c49a732770a4970896305047fee84c7db21a22a9a3d079830"],"state_sha256":"e7605c33d1b6563edfe597c0e7936d49e5c6e143ef6b556d3bb8af396081c1f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qG+6c4vMzNPIzlMuXEQfmEMlBpXlbk8j4aBYB2WWYCXoVouZSTl0YrjWxOdShVPebLfitYVVtQ9HprXt1S5kDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T00:53:28.018653Z","bundle_sha256":"61deda4d00e296ce0b540afa180a8318b3e7b5476e6b6d7189a24d4d6607cbf2"}}