{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:LTETBD67BMNLJHM6TI66TMRKON","short_pith_number":"pith:LTETBD67","canonical_record":{"source":{"id":"1806.05136","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-06-13T16:34:56Z","cross_cats_sorted":[],"title_canon_sha256":"0d4c1a7d43ec648f5fef09d640053d9de704370c47cb6ab0bef210986e73bdca","abstract_canon_sha256":"d8b65f8fc7f1eacd3db95b8e3435ba028ce4891dab4e4c6839048c7e5fd50a75"},"schema_version":"1.0"},"canonical_sha256":"5cc9308fdf0b1ab49d9e9a3de9b22a7353bb3f1988e49386b881d34a58fd565d","source":{"kind":"arxiv","id":"1806.05136","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05136","created_at":"2026-05-18T00:13:20Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05136v1","created_at":"2026-05-18T00:13:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05136","created_at":"2026-05-18T00:13:20Z"},{"alias_kind":"pith_short_12","alias_value":"LTETBD67BMNL","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LTETBD67BMNLJHM6","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LTETBD67","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:LTETBD67BMNLJHM6TI66TMRKON","target":"record","payload":{"canonical_record":{"source":{"id":"1806.05136","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-06-13T16:34:56Z","cross_cats_sorted":[],"title_canon_sha256":"0d4c1a7d43ec648f5fef09d640053d9de704370c47cb6ab0bef210986e73bdca","abstract_canon_sha256":"d8b65f8fc7f1eacd3db95b8e3435ba028ce4891dab4e4c6839048c7e5fd50a75"},"schema_version":"1.0"},"canonical_sha256":"5cc9308fdf0b1ab49d9e9a3de9b22a7353bb3f1988e49386b881d34a58fd565d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:20.070054Z","signature_b64":"O86ELxUeVta/TztEn24rbP9sEELoROl7yUWyDa74WxkJoSdcB4/pbSN3Z6WEa8TtNL/msAV5OQsp8FNReXUPDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cc9308fdf0b1ab49d9e9a3de9b22a7353bb3f1988e49386b881d34a58fd565d","last_reissued_at":"2026-05-18T00:13:20.069464Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:20.069464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.05136","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":"2026-05-18T00:13:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zVZ/HwZnHOih9sROj2UK83uFNqWMt+5hRQ09x+YDcIb1JtEtuoZg2oBxeDMLWJV9jv4NxHOTLv5j2rRWTv6/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:50:23.309646Z"},"content_sha256":"67e6b5b19fd17ab59dbc0dec92200eb662f74b5fa1ea774258ba1e74544643e2","schema_version":"1.0","event_id":"sha256:67e6b5b19fd17ab59dbc0dec92200eb662f74b5fa1ea774258ba1e74544643e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:LTETBD67BMNLJHM6TI66TMRKON","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Starlikeness associated with lemniscate of Bernoulli","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Ajay Kumar, Vibha Madaan, V. Ravichandran","submitted_at":"2018-06-13T16:34:56Z","abstract_excerpt":"For an analytic function $f$ on the unit disk $\\mathbb{D}=\\{z:|z|<1\\}$ satisfying $f(0)=0=f'(0)-1,$ we obtain sufficient conditions so that $f$ satisfies $|(zf'(z)/f(z))^2-1|<1.$ The technique of differential subordination of first or second order is used. The admissibility conditions for lemniscate of Bernoulli are derived and employed in order to prove the main results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05136","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":"2026-05-18T00:13:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c1WIFfeuuU2k3dFYmaCf5jLUOvh6zgBd+CqOVt1kKoXnOV8o7CcLDkcCrVPegL12zAGROjdxas/L5+u8qxaJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:50:23.309990Z"},"content_sha256":"93a0fdf0800b171e7318ee5fef2d974cea04a1b420e20835919bc09d607327c6","schema_version":"1.0","event_id":"sha256:93a0fdf0800b171e7318ee5fef2d974cea04a1b420e20835919bc09d607327c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LTETBD67BMNLJHM6TI66TMRKON/bundle.json","state_url":"https://pith.science/pith/LTETBD67BMNLJHM6TI66TMRKON/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LTETBD67BMNLJHM6TI66TMRKON/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":"2026-06-20T08:50:23Z","links":{"resolver":"https://pith.science/pith/LTETBD67BMNLJHM6TI66TMRKON","bundle":"https://pith.science/pith/LTETBD67BMNLJHM6TI66TMRKON/bundle.json","state":"https://pith.science/pith/LTETBD67BMNLJHM6TI66TMRKON/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LTETBD67BMNLJHM6TI66TMRKON/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LTETBD67BMNLJHM6TI66TMRKON","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":"d8b65f8fc7f1eacd3db95b8e3435ba028ce4891dab4e4c6839048c7e5fd50a75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-06-13T16:34:56Z","title_canon_sha256":"0d4c1a7d43ec648f5fef09d640053d9de704370c47cb6ab0bef210986e73bdca"},"schema_version":"1.0","source":{"id":"1806.05136","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05136","created_at":"2026-05-18T00:13:20Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05136v1","created_at":"2026-05-18T00:13:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05136","created_at":"2026-05-18T00:13:20Z"},{"alias_kind":"pith_short_12","alias_value":"LTETBD67BMNL","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LTETBD67BMNLJHM6","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LTETBD67","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:93a0fdf0800b171e7318ee5fef2d974cea04a1b420e20835919bc09d607327c6","target":"graph","created_at":"2026-05-18T00:13:20Z","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 $f$ on the unit disk $\\mathbb{D}=\\{z:|z|<1\\}$ satisfying $f(0)=0=f'(0)-1,$ we obtain sufficient conditions so that $f$ satisfies $|(zf'(z)/f(z))^2-1|<1.$ The technique of differential subordination of first or second order is used. The admissibility conditions for lemniscate of Bernoulli are derived and employed in order to prove the main results.","authors_text":"Ajay Kumar, Vibha Madaan, V. Ravichandran","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-06-13T16:34:56Z","title":"Starlikeness associated with lemniscate of Bernoulli"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05136","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":"sha256:67e6b5b19fd17ab59dbc0dec92200eb662f74b5fa1ea774258ba1e74544643e2","target":"record","created_at":"2026-05-18T00:13:20Z","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":"d8b65f8fc7f1eacd3db95b8e3435ba028ce4891dab4e4c6839048c7e5fd50a75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-06-13T16:34:56Z","title_canon_sha256":"0d4c1a7d43ec648f5fef09d640053d9de704370c47cb6ab0bef210986e73bdca"},"schema_version":"1.0","source":{"id":"1806.05136","kind":"arxiv","version":1}},"canonical_sha256":"5cc9308fdf0b1ab49d9e9a3de9b22a7353bb3f1988e49386b881d34a58fd565d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cc9308fdf0b1ab49d9e9a3de9b22a7353bb3f1988e49386b881d34a58fd565d","first_computed_at":"2026-05-18T00:13:20.069464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:20.069464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O86ELxUeVta/TztEn24rbP9sEELoROl7yUWyDa74WxkJoSdcB4/pbSN3Z6WEa8TtNL/msAV5OQsp8FNReXUPDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:20.070054Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.05136","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67e6b5b19fd17ab59dbc0dec92200eb662f74b5fa1ea774258ba1e74544643e2","sha256:93a0fdf0800b171e7318ee5fef2d974cea04a1b420e20835919bc09d607327c6"],"state_sha256":"3dffe520f0278d6753ca57a71b65ec4be7504d4911fb9ff9019acebaaabe34de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2dkK4VNfqmB3Fq5d6o/lfQNAVKi3lLv7f8Gd05/MeVYgr6qj+qj95PH3FTGSUXH3BUsNPPndGoYKM/mfvKJ/DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T08:50:23.311933Z","bundle_sha256":"9d184290a256dade2043907faf9306a2e63e5d16686f15af7a18f19dc6ea2c32"}}