{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TR5M6SZ32B5KHZUG6Y4PRSNOPX","short_pith_number":"pith:TR5M6SZ3","canonical_record":{"source":{"id":"1108.5418","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-08-27T05:02:31Z","cross_cats_sorted":[],"title_canon_sha256":"21fe2da81ff8358978e6c0e14db60b21288da8203ae1472b8e285c9e4a5ed3a1","abstract_canon_sha256":"428357a12ae5dbd17db9b032cad7f9c68942a0481335c60ed6e4787372b4ee6d"},"schema_version":"1.0"},"canonical_sha256":"9c7acf4b3bd07aa3e686f638f8c9ae7dd9cdea215c8e959529bc49aa3c7b52b1","source":{"kind":"arxiv","id":"1108.5418","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5418","created_at":"2026-05-18T04:05:05Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5418v1","created_at":"2026-05-18T04:05:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5418","created_at":"2026-05-18T04:05:05Z"},{"alias_kind":"pith_short_12","alias_value":"TR5M6SZ32B5K","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TR5M6SZ32B5KHZUG","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TR5M6SZ3","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TR5M6SZ32B5KHZUG6Y4PRSNOPX","target":"record","payload":{"canonical_record":{"source":{"id":"1108.5418","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-08-27T05:02:31Z","cross_cats_sorted":[],"title_canon_sha256":"21fe2da81ff8358978e6c0e14db60b21288da8203ae1472b8e285c9e4a5ed3a1","abstract_canon_sha256":"428357a12ae5dbd17db9b032cad7f9c68942a0481335c60ed6e4787372b4ee6d"},"schema_version":"1.0"},"canonical_sha256":"9c7acf4b3bd07aa3e686f638f8c9ae7dd9cdea215c8e959529bc49aa3c7b52b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:05.171623Z","signature_b64":"ShRr7FD6kE1MZGuNPDnCYR0/ykJ4VTp1Wo+kAbtjyhQBQo8QKS2Gif75JKbI51+KO0em6yBnoCBJ3qo+ZBvIAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c7acf4b3bd07aa3e686f638f8c9ae7dd9cdea215c8e959529bc49aa3c7b52b1","last_reissued_at":"2026-05-18T04:05:05.171087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:05.171087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.5418","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":"2026-05-18T04:05:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x0e1QOc8sT522BEXtjsW8FBRs0CEzl0QtCcooQa93lZUdsUIIJ1k+wZgikmU2CEox7HOlgOn2UAGiH5JOSFVBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:28:29.136078Z"},"content_sha256":"ad36dc244756c57689318c977db523f9cd2f644bb0431157f297b11799553107","schema_version":"1.0","event_id":"sha256:ad36dc244756c57689318c977db523f9cd2f644bb0431157f297b11799553107"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TR5M6SZ32B5KHZUG6Y4PRSNOPX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Radii of Starlikeness Associated with the Lemniscate of Bernoulli and the Left-Half Plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Naveen Jain, Rosihan M. Ali, V. Ravichandran","submitted_at":"2011-08-27T05:02:31Z","abstract_excerpt":"A normalized analytic function f defined on the open unit disk in the complex plane is in the class SL if zf'(z)/f(z) lies in the region bounded by the right-half of the lemniscate of Bernoulli given by |w^2 - 1| < 1. In the present investigation, the SL-radii for certain well-known classes of functions are obtained. Radius problems associated with the left-half plane are also investigated for these classes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5418","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":"2026-05-18T04:05:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p4/zLG2RHUwLTH+hYG1DeFgr5FttXPe4kJeLLwfe7XGpqd9p6nTZxkRmagyrtd8iejRCiROSL6F2dDCkyyAMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:28:29.136768Z"},"content_sha256":"291e24cf971255507660d1bd57e5c227561a37f8e0f26083e1372cb87173f228","schema_version":"1.0","event_id":"sha256:291e24cf971255507660d1bd57e5c227561a37f8e0f26083e1372cb87173f228"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TR5M6SZ32B5KHZUG6Y4PRSNOPX/bundle.json","state_url":"https://pith.science/pith/TR5M6SZ32B5KHZUG6Y4PRSNOPX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TR5M6SZ32B5KHZUG6Y4PRSNOPX/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":"2026-06-05T20:28:29Z","links":{"resolver":"https://pith.science/pith/TR5M6SZ32B5KHZUG6Y4PRSNOPX","bundle":"https://pith.science/pith/TR5M6SZ32B5KHZUG6Y4PRSNOPX/bundle.json","state":"https://pith.science/pith/TR5M6SZ32B5KHZUG6Y4PRSNOPX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TR5M6SZ32B5KHZUG6Y4PRSNOPX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TR5M6SZ32B5KHZUG6Y4PRSNOPX","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":"428357a12ae5dbd17db9b032cad7f9c68942a0481335c60ed6e4787372b4ee6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-08-27T05:02:31Z","title_canon_sha256":"21fe2da81ff8358978e6c0e14db60b21288da8203ae1472b8e285c9e4a5ed3a1"},"schema_version":"1.0","source":{"id":"1108.5418","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5418","created_at":"2026-05-18T04:05:05Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5418v1","created_at":"2026-05-18T04:05:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5418","created_at":"2026-05-18T04:05:05Z"},{"alias_kind":"pith_short_12","alias_value":"TR5M6SZ32B5K","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TR5M6SZ32B5KHZUG","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TR5M6SZ3","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:291e24cf971255507660d1bd57e5c227561a37f8e0f26083e1372cb87173f228","target":"graph","created_at":"2026-05-18T04:05:05Z","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":"A normalized analytic function f defined on the open unit disk in the complex plane is in the class SL if zf'(z)/f(z) lies in the region bounded by the right-half of the lemniscate of Bernoulli given by |w^2 - 1| < 1. In the present investigation, the SL-radii for certain well-known classes of functions are obtained. Radius problems associated with the left-half plane are also investigated for these classes","authors_text":"Naveen Jain, Rosihan M. Ali, V. Ravichandran","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-08-27T05:02:31Z","title":"Radii of Starlikeness Associated with the Lemniscate of Bernoulli and the Left-Half Plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5418","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:ad36dc244756c57689318c977db523f9cd2f644bb0431157f297b11799553107","target":"record","created_at":"2026-05-18T04:05:05Z","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":"428357a12ae5dbd17db9b032cad7f9c68942a0481335c60ed6e4787372b4ee6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-08-27T05:02:31Z","title_canon_sha256":"21fe2da81ff8358978e6c0e14db60b21288da8203ae1472b8e285c9e4a5ed3a1"},"schema_version":"1.0","source":{"id":"1108.5418","kind":"arxiv","version":1}},"canonical_sha256":"9c7acf4b3bd07aa3e686f638f8c9ae7dd9cdea215c8e959529bc49aa3c7b52b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c7acf4b3bd07aa3e686f638f8c9ae7dd9cdea215c8e959529bc49aa3c7b52b1","first_computed_at":"2026-05-18T04:05:05.171087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:05.171087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ShRr7FD6kE1MZGuNPDnCYR0/ykJ4VTp1Wo+kAbtjyhQBQo8QKS2Gif75JKbI51+KO0em6yBnoCBJ3qo+ZBvIAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:05.171623Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5418","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad36dc244756c57689318c977db523f9cd2f644bb0431157f297b11799553107","sha256:291e24cf971255507660d1bd57e5c227561a37f8e0f26083e1372cb87173f228"],"state_sha256":"611a9f1a317a80edb187c3f419ba113cbe4675b014d9875eead6b233e3fdbfee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SNNq1qdB6tPjsaxcln+FXPe9zV0ioOf9rJHs0gywUNuW9MHgo5SIdsLNUBS2Pe6lbKC4WJWRzaWHLO8+27xzCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T20:28:29.140186Z","bundle_sha256":"7835b8ac7168e4c08a8431c66a0ff6e016a0381a35d2144670c986772fce8a25"}}