{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:N27TQETFRPJJJXHYDIKW42OEUU","short_pith_number":"pith:N27TQETF","canonical_record":{"source":{"id":"1810.03839","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-10-09T07:49:50Z","cross_cats_sorted":[],"title_canon_sha256":"0ab1e8a2233210e281dbda703408b14b3d98ddae8ae3a4aa30387eab7f9c1319","abstract_canon_sha256":"46382cc628c50a7384fc09b714a7522b5c0fbf1fd514722d7d29141a8f7e4a7a"},"schema_version":"1.0"},"canonical_sha256":"6ebf3812658bd294dcf81a156e69c4a5331d69d0a22ef757340d83c3d26be58a","source":{"kind":"arxiv","id":"1810.03839","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03839","created_at":"2026-05-18T00:03:14Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03839v2","created_at":"2026-05-18T00:03:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03839","created_at":"2026-05-18T00:03:14Z"},{"alias_kind":"pith_short_12","alias_value":"N27TQETFRPJJ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"N27TQETFRPJJJXHY","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"N27TQETF","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:N27TQETFRPJJJXHYDIKW42OEUU","target":"record","payload":{"canonical_record":{"source":{"id":"1810.03839","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-10-09T07:49:50Z","cross_cats_sorted":[],"title_canon_sha256":"0ab1e8a2233210e281dbda703408b14b3d98ddae8ae3a4aa30387eab7f9c1319","abstract_canon_sha256":"46382cc628c50a7384fc09b714a7522b5c0fbf1fd514722d7d29141a8f7e4a7a"},"schema_version":"1.0"},"canonical_sha256":"6ebf3812658bd294dcf81a156e69c4a5331d69d0a22ef757340d83c3d26be58a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:14.455494Z","signature_b64":"u3vVp7WQW0OnBIRqifEPzBi5Zv36eusDkhKzZRw4iAIklRf1D7mYv59g1uAIgxP/A/TIa93I0Igsjr1CNR+sBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ebf3812658bd294dcf81a156e69c4a5331d69d0a22ef757340d83c3d26be58a","last_reissued_at":"2026-05-18T00:03:14.454779Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:14.454779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.03839","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:03:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IkNo3tb1jKj4QUVbGeByzg4JSUSoJnTo1TAniKUgiYM2qidA47pqMlxeVJo+ppEffkj134dcKO35N/SXZevXAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:37:50.364150Z"},"content_sha256":"4a2ae57950ae1da0c777ec96d7c9ceacc303b20285dece68cd197335ef23eb75","schema_version":"1.0","event_id":"sha256:4a2ae57950ae1da0c777ec96d7c9ceacc303b20285dece68cd197335ef23eb75"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:N27TQETFRPJJJXHYDIKW42OEUU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A class of univalent functions with real coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Milutin Obradovic, Nikola Tuneski","submitted_at":"2018-10-09T07:49:50Z","abstract_excerpt":"In this paper we study class $\\mathcal{S}^+$ of univalent functions $f$ such that $\\frac{z}{f(z)}$ has real and positive coefficients. For such functions we give estimates of the Fekete-Szeg\\H{o} functional and sharp estimates of their initial coefficients and logarithmic coefficients. Also, we present necessary and sufficient conditions for $f\\in \\mathcal{S}^+$ to be starlike of order $1/2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03839","kind":"arxiv","version":2},"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":"2026-05-18T00:03:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b/ZKWGYG5AC1d2PCrsvqCDGvhvXDanTBgVPLPD9qroOP1HQWRWB68tpxCzoPKvzCraqVXVqRQzPslBjL7KQGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:37:50.364513Z"},"content_sha256":"06b4db42aab1434fd999177a07852fd4cb80bdd6f6bbf92ad46bec26839fc7a1","schema_version":"1.0","event_id":"sha256:06b4db42aab1434fd999177a07852fd4cb80bdd6f6bbf92ad46bec26839fc7a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N27TQETFRPJJJXHYDIKW42OEUU/bundle.json","state_url":"https://pith.science/pith/N27TQETFRPJJJXHYDIKW42OEUU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N27TQETFRPJJJXHYDIKW42OEUU/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":"2026-06-01T12:37:50Z","links":{"resolver":"https://pith.science/pith/N27TQETFRPJJJXHYDIKW42OEUU","bundle":"https://pith.science/pith/N27TQETFRPJJJXHYDIKW42OEUU/bundle.json","state":"https://pith.science/pith/N27TQETFRPJJJXHYDIKW42OEUU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N27TQETFRPJJJXHYDIKW42OEUU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:N27TQETFRPJJJXHYDIKW42OEUU","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":"46382cc628c50a7384fc09b714a7522b5c0fbf1fd514722d7d29141a8f7e4a7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-10-09T07:49:50Z","title_canon_sha256":"0ab1e8a2233210e281dbda703408b14b3d98ddae8ae3a4aa30387eab7f9c1319"},"schema_version":"1.0","source":{"id":"1810.03839","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03839","created_at":"2026-05-18T00:03:14Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03839v2","created_at":"2026-05-18T00:03:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03839","created_at":"2026-05-18T00:03:14Z"},{"alias_kind":"pith_short_12","alias_value":"N27TQETFRPJJ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"N27TQETFRPJJJXHY","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"N27TQETF","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:06b4db42aab1434fd999177a07852fd4cb80bdd6f6bbf92ad46bec26839fc7a1","target":"graph","created_at":"2026-05-18T00:03:14Z","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":"In this paper we study class $\\mathcal{S}^+$ of univalent functions $f$ such that $\\frac{z}{f(z)}$ has real and positive coefficients. For such functions we give estimates of the Fekete-Szeg\\H{o} functional and sharp estimates of their initial coefficients and logarithmic coefficients. Also, we present necessary and sufficient conditions for $f\\in \\mathcal{S}^+$ to be starlike of order $1/2$.","authors_text":"Milutin Obradovic, Nikola Tuneski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-10-09T07:49:50Z","title":"A class of univalent functions with real coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03839","kind":"arxiv","version":2},"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":"sha256:4a2ae57950ae1da0c777ec96d7c9ceacc303b20285dece68cd197335ef23eb75","target":"record","created_at":"2026-05-18T00:03:14Z","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":"46382cc628c50a7384fc09b714a7522b5c0fbf1fd514722d7d29141a8f7e4a7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-10-09T07:49:50Z","title_canon_sha256":"0ab1e8a2233210e281dbda703408b14b3d98ddae8ae3a4aa30387eab7f9c1319"},"schema_version":"1.0","source":{"id":"1810.03839","kind":"arxiv","version":2}},"canonical_sha256":"6ebf3812658bd294dcf81a156e69c4a5331d69d0a22ef757340d83c3d26be58a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ebf3812658bd294dcf81a156e69c4a5331d69d0a22ef757340d83c3d26be58a","first_computed_at":"2026-05-18T00:03:14.454779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:14.454779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u3vVp7WQW0OnBIRqifEPzBi5Zv36eusDkhKzZRw4iAIklRf1D7mYv59g1uAIgxP/A/TIa93I0Igsjr1CNR+sBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:14.455494Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.03839","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a2ae57950ae1da0c777ec96d7c9ceacc303b20285dece68cd197335ef23eb75","sha256:06b4db42aab1434fd999177a07852fd4cb80bdd6f6bbf92ad46bec26839fc7a1"],"state_sha256":"f5471e1c488ecbbe114db7720578e43d36005495002f3e3c1578806ded1096a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HQXk7YxR0GnldqBLBrJOUUcuWCqSMyQAbtQaNuJE/WcjOmnFng0WujuFeBlxIC02OCsllvafzoAXHldG2OwRAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:37:50.366531Z","bundle_sha256":"56039277f72d1df525f393880f334f56cea925745e0b50e3fb245504931af3ae"}}