{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:L5XKIS4YWAXMLBGJROITSDUNMF","short_pith_number":"pith:L5XKIS4Y","canonical_record":{"source":{"id":"2411.12378","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2024-11-19T09:55:15Z","cross_cats_sorted":[],"title_canon_sha256":"0a3a494e775523485e6a031ddabd26a3ae077361262eddceb0dfc75f8341a7cf","abstract_canon_sha256":"9a9e4119f395d61d528bf9ef683f1ceb8697bb4b89dac8510d5eb369e9ff75b3"},"schema_version":"1.0"},"canonical_sha256":"5f6ea44b98b02ec584c98b91390e8d61641e96472220c22829d055b5f8a13860","source":{"kind":"arxiv","id":"2411.12378","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.12378","created_at":"2026-07-05T09:37:20Z"},{"alias_kind":"arxiv_version","alias_value":"2411.12378v1","created_at":"2026-07-05T09:37:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.12378","created_at":"2026-07-05T09:37:20Z"},{"alias_kind":"pith_short_12","alias_value":"L5XKIS4YWAXM","created_at":"2026-07-05T09:37:20Z"},{"alias_kind":"pith_short_16","alias_value":"L5XKIS4YWAXMLBGJ","created_at":"2026-07-05T09:37:20Z"},{"alias_kind":"pith_short_8","alias_value":"L5XKIS4Y","created_at":"2026-07-05T09:37:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:L5XKIS4YWAXMLBGJROITSDUNMF","target":"record","payload":{"canonical_record":{"source":{"id":"2411.12378","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2024-11-19T09:55:15Z","cross_cats_sorted":[],"title_canon_sha256":"0a3a494e775523485e6a031ddabd26a3ae077361262eddceb0dfc75f8341a7cf","abstract_canon_sha256":"9a9e4119f395d61d528bf9ef683f1ceb8697bb4b89dac8510d5eb369e9ff75b3"},"schema_version":"1.0"},"canonical_sha256":"5f6ea44b98b02ec584c98b91390e8d61641e96472220c22829d055b5f8a13860","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:37:20.539270Z","signature_b64":"KORARHb+e9suHtcAwwaLCIK7NACugCZ9ss3/DbA0ymQ6HYll/82BNcopAgZbcsIE68GcdF2goO/e4CCmikRLBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f6ea44b98b02ec584c98b91390e8d61641e96472220c22829d055b5f8a13860","last_reissued_at":"2026-07-05T09:37:20.538787Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:37:20.538787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.12378","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":"2026-07-05T09:37:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AQXTydrOB2XWnJc5m/wtwIoB3NOETHbGcZpmkJorIXa+uMHSlADvFZRLEfnq8cpwqaeXgiHqgZzVKXF0IXGSBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:44:51.922560Z"},"content_sha256":"8f14910b4923d4179a55ddad652a8a76f8bb4f088b61da4baf08c4b90eea688d","schema_version":"1.0","event_id":"sha256:8f14910b4923d4179a55ddad652a8a76f8bb4f088b61da4baf08c4b90eea688d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:L5XKIS4YWAXMLBGJROITSDUNMF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An improvement of the estimates of the modulus of the Hankel determinants of second and third order for the class $\\mathcal{S}$ of univalent functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Milutin Obradovi\\'c, Nikola Tuneski","submitted_at":"2024-11-19T09:55:15Z","abstract_excerpt":"Using some properties of the Grunsky coefficients we improve earlier results for upper bounds of the Hankel determinants of the second and third order for the class $\\mathcal{S}$ of univalent functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12378","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.12378/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:37:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qvhg4EJE1ZHM13gqxhGS2lLjTalqa8izbz+PfRB5v9h0pGyudFqjc/snyRdOxE9I1OAmZ24gPS9RVdicTeriAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:44:51.923507Z"},"content_sha256":"c4dbe08660803b868d2566f4fc6198b921e372328278c9d9f3946f098f91067e","schema_version":"1.0","event_id":"sha256:c4dbe08660803b868d2566f4fc6198b921e372328278c9d9f3946f098f91067e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L5XKIS4YWAXMLBGJROITSDUNMF/bundle.json","state_url":"https://pith.science/pith/L5XKIS4YWAXMLBGJROITSDUNMF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L5XKIS4YWAXMLBGJROITSDUNMF/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":"2026-08-13T09:44:52Z","links":{"resolver":"https://pith.science/pith/L5XKIS4YWAXMLBGJROITSDUNMF","bundle":"https://pith.science/pith/L5XKIS4YWAXMLBGJROITSDUNMF/bundle.json","state":"https://pith.science/pith/L5XKIS4YWAXMLBGJROITSDUNMF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L5XKIS4YWAXMLBGJROITSDUNMF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:L5XKIS4YWAXMLBGJROITSDUNMF","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":"9a9e4119f395d61d528bf9ef683f1ceb8697bb4b89dac8510d5eb369e9ff75b3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2024-11-19T09:55:15Z","title_canon_sha256":"0a3a494e775523485e6a031ddabd26a3ae077361262eddceb0dfc75f8341a7cf"},"schema_version":"1.0","source":{"id":"2411.12378","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.12378","created_at":"2026-07-05T09:37:20Z"},{"alias_kind":"arxiv_version","alias_value":"2411.12378v1","created_at":"2026-07-05T09:37:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.12378","created_at":"2026-07-05T09:37:20Z"},{"alias_kind":"pith_short_12","alias_value":"L5XKIS4YWAXM","created_at":"2026-07-05T09:37:20Z"},{"alias_kind":"pith_short_16","alias_value":"L5XKIS4YWAXMLBGJ","created_at":"2026-07-05T09:37:20Z"},{"alias_kind":"pith_short_8","alias_value":"L5XKIS4Y","created_at":"2026-07-05T09:37:20Z"}],"graph_snapshots":[{"event_id":"sha256:c4dbe08660803b868d2566f4fc6198b921e372328278c9d9f3946f098f91067e","target":"graph","created_at":"2026-07-05T09:37:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.12378/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Using some properties of the Grunsky coefficients we improve earlier results for upper bounds of the Hankel determinants of the second and third order for the class $\\mathcal{S}$ of univalent functions.","authors_text":"Milutin Obradovi\\'c, Nikola Tuneski","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2024-11-19T09:55:15Z","title":"An improvement of the estimates of the modulus of the Hankel determinants of second and third order for the class $\\mathcal{S}$ of univalent functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12378","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":"sha256:8f14910b4923d4179a55ddad652a8a76f8bb4f088b61da4baf08c4b90eea688d","target":"record","created_at":"2026-07-05T09:37:20Z","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":"9a9e4119f395d61d528bf9ef683f1ceb8697bb4b89dac8510d5eb369e9ff75b3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2024-11-19T09:55:15Z","title_canon_sha256":"0a3a494e775523485e6a031ddabd26a3ae077361262eddceb0dfc75f8341a7cf"},"schema_version":"1.0","source":{"id":"2411.12378","kind":"arxiv","version":1}},"canonical_sha256":"5f6ea44b98b02ec584c98b91390e8d61641e96472220c22829d055b5f8a13860","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f6ea44b98b02ec584c98b91390e8d61641e96472220c22829d055b5f8a13860","first_computed_at":"2026-07-05T09:37:20.538787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:37:20.538787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KORARHb+e9suHtcAwwaLCIK7NACugCZ9ss3/DbA0ymQ6HYll/82BNcopAgZbcsIE68GcdF2goO/e4CCmikRLBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:37:20.539270Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.12378","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f14910b4923d4179a55ddad652a8a76f8bb4f088b61da4baf08c4b90eea688d","sha256:c4dbe08660803b868d2566f4fc6198b921e372328278c9d9f3946f098f91067e"],"state_sha256":"57c284526b0c423debcf1d1835af80c2d4a801ab64de4180ac8869daadc17c08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rVbhUiQfd+D3YkRGmxdIOhoF/OuxjnCiB5uJAaesWoRI/f2LYujWl+EOgCF+Y9cnSjMXa3GNZFkkKnA9M3rfBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T09:44:52.029900Z","bundle_sha256":"0b3aced342b7bcbb6ea59108df03521bde17c39aff1f7e936a9ae7d5d032dfdf"}}