{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7ZTFQX7VAOXNPI5PYK3V5NELTZ","short_pith_number":"pith:7ZTFQX7V","canonical_record":{"source":{"id":"1303.0506","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-03T14:27:14Z","cross_cats_sorted":[],"title_canon_sha256":"650da04daae09d9e228914b5dbbe1c9901ddfe269b35c135143409e183ab218d","abstract_canon_sha256":"b6f2a8aa3471f6d9f755ed110a81f8cd2dbfa93fcc5c7a9c77793d6303d84a58"},"schema_version":"1.0"},"canonical_sha256":"fe66585ff503aed7a3afc2b75eb48b9e7ed7adf7cdafbdda066992ae0908bf53","source":{"kind":"arxiv","id":"1303.0506","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0506","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0506v1","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0506","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"pith_short_12","alias_value":"7ZTFQX7VAOXN","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7ZTFQX7VAOXNPI5P","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7ZTFQX7V","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7ZTFQX7VAOXNPI5PYK3V5NELTZ","target":"record","payload":{"canonical_record":{"source":{"id":"1303.0506","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-03T14:27:14Z","cross_cats_sorted":[],"title_canon_sha256":"650da04daae09d9e228914b5dbbe1c9901ddfe269b35c135143409e183ab218d","abstract_canon_sha256":"b6f2a8aa3471f6d9f755ed110a81f8cd2dbfa93fcc5c7a9c77793d6303d84a58"},"schema_version":"1.0"},"canonical_sha256":"fe66585ff503aed7a3afc2b75eb48b9e7ed7adf7cdafbdda066992ae0908bf53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:55.721677Z","signature_b64":"48LSJWMKolKKoqvp6besQUi0oNnnIAyUeCXFHqMyYyLxXvlca8xC5sTgflrqE/nlGdamo0PDf/bsSCvgYv+UDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe66585ff503aed7a3afc2b75eb48b9e7ed7adf7cdafbdda066992ae0908bf53","last_reissued_at":"2026-05-18T03:31:55.720694Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:55.720694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.0506","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":"2026-05-18T03:31:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bC97h44mycJfE2EQRAbrdfWQyVDeRqq0H7XBCymBy3ScBmKdWKXdIPocFpZreadA1XJ7PYu16bz3m545RmQ6CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:25:28.425099Z"},"content_sha256":"2a52b95def1e87cbaec200d22e4aa364117051e98bcfa2311db0c485b49147de","schema_version":"1.0","event_id":"sha256:2a52b95def1e87cbaec200d22e4aa364117051e98bcfa2311db0c485b49147de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7ZTFQX7VAOXNPI5PYK3V5NELTZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Properties of certain analytic functions associated with two boundary points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Hitoshi Shiraishi, Shigeyoshi Owa","submitted_at":"2013-03-03T14:27:14Z","abstract_excerpt":"For analytic functions f(z) in the closed unit disk \\bar{U}, two boundary points z_1 and z_2 such that \\alpha = (f'(z_1)+f'(z_2))/2 in f'(U) are considered. The object of the present paper is to discuss some interesting conditions for f(z) to be |f'(z)-1|<\\rho|1-\\alpha| in U with some examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0506","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":"2026-05-18T03:31:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KwRtz6Edxo1lzg2rk4N8kZnTdrNCIBIZKiaOEt7g/4FHnEn9V0hhqpJZ0NHwl+tHR6nTBHEU8lt66cJTbR2qCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:25:28.425492Z"},"content_sha256":"111f35fb7c24b36ada12eaef19a1887412cc5894cf54a0ca656fa46ad0624f4b","schema_version":"1.0","event_id":"sha256:111f35fb7c24b36ada12eaef19a1887412cc5894cf54a0ca656fa46ad0624f4b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7ZTFQX7VAOXNPI5PYK3V5NELTZ/bundle.json","state_url":"https://pith.science/pith/7ZTFQX7VAOXNPI5PYK3V5NELTZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7ZTFQX7VAOXNPI5PYK3V5NELTZ/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":"2026-06-22T14:25:28Z","links":{"resolver":"https://pith.science/pith/7ZTFQX7VAOXNPI5PYK3V5NELTZ","bundle":"https://pith.science/pith/7ZTFQX7VAOXNPI5PYK3V5NELTZ/bundle.json","state":"https://pith.science/pith/7ZTFQX7VAOXNPI5PYK3V5NELTZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7ZTFQX7VAOXNPI5PYK3V5NELTZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7ZTFQX7VAOXNPI5PYK3V5NELTZ","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":"b6f2a8aa3471f6d9f755ed110a81f8cd2dbfa93fcc5c7a9c77793d6303d84a58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-03T14:27:14Z","title_canon_sha256":"650da04daae09d9e228914b5dbbe1c9901ddfe269b35c135143409e183ab218d"},"schema_version":"1.0","source":{"id":"1303.0506","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0506","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0506v1","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0506","created_at":"2026-05-18T03:31:55Z"},{"alias_kind":"pith_short_12","alias_value":"7ZTFQX7VAOXN","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7ZTFQX7VAOXNPI5P","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7ZTFQX7V","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:111f35fb7c24b36ada12eaef19a1887412cc5894cf54a0ca656fa46ad0624f4b","target":"graph","created_at":"2026-05-18T03:31:55Z","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 analytic functions f(z) in the closed unit disk \\bar{U}, two boundary points z_1 and z_2 such that \\alpha = (f'(z_1)+f'(z_2))/2 in f'(U) are considered. The object of the present paper is to discuss some interesting conditions for f(z) to be |f'(z)-1|<\\rho|1-\\alpha| in U with some examples.","authors_text":"Hitoshi Shiraishi, Shigeyoshi Owa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-03T14:27:14Z","title":"Properties of certain analytic functions associated with two boundary points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0506","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":"sha256:2a52b95def1e87cbaec200d22e4aa364117051e98bcfa2311db0c485b49147de","target":"record","created_at":"2026-05-18T03:31:55Z","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":"b6f2a8aa3471f6d9f755ed110a81f8cd2dbfa93fcc5c7a9c77793d6303d84a58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-03T14:27:14Z","title_canon_sha256":"650da04daae09d9e228914b5dbbe1c9901ddfe269b35c135143409e183ab218d"},"schema_version":"1.0","source":{"id":"1303.0506","kind":"arxiv","version":1}},"canonical_sha256":"fe66585ff503aed7a3afc2b75eb48b9e7ed7adf7cdafbdda066992ae0908bf53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe66585ff503aed7a3afc2b75eb48b9e7ed7adf7cdafbdda066992ae0908bf53","first_computed_at":"2026-05-18T03:31:55.720694Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:55.720694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"48LSJWMKolKKoqvp6besQUi0oNnnIAyUeCXFHqMyYyLxXvlca8xC5sTgflrqE/nlGdamo0PDf/bsSCvgYv+UDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:55.721677Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.0506","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a52b95def1e87cbaec200d22e4aa364117051e98bcfa2311db0c485b49147de","sha256:111f35fb7c24b36ada12eaef19a1887412cc5894cf54a0ca656fa46ad0624f4b"],"state_sha256":"7df0c87466355590c11e09d06580043d8c73e154be50f8cdf7ba7eab7dd884dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gGXLcLdlMyJvfDRyYa8mE45ftYJ0fdaI6LPbM170Isxu4jBFEf4cAyp/qMWtTmKWBym8dJ8DfSIhBFHB4AQsCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T14:25:28.427514Z","bundle_sha256":"7d14c0ade1910505df8c927352849f176b7b1427dafc4c3ffacd25be8b964dfa"}}