{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:P77F5VRCGPAWDQRB4UVQXROM4K","short_pith_number":"pith:P77F5VRC","canonical_record":{"source":{"id":"1302.6903","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-27T16:20:34Z","cross_cats_sorted":[],"title_canon_sha256":"49e6bc5f9ed993c591c38fcdc6cf11a2c8c36d187cd3b699e04579eb64bb17e5","abstract_canon_sha256":"ebdb1bf81dfc1ca43686f6fcbfc56112af07819ffd3116602dc2b8c78cdbf65c"},"schema_version":"1.0"},"canonical_sha256":"7ffe5ed62233c161c221e52b0bc5cce2a448468876ec70fb8106ec103d751427","source":{"kind":"arxiv","id":"1302.6903","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6903","created_at":"2026-05-18T03:32:18Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6903v1","created_at":"2026-05-18T03:32:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6903","created_at":"2026-05-18T03:32:18Z"},{"alias_kind":"pith_short_12","alias_value":"P77F5VRCGPAW","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P77F5VRCGPAWDQRB","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P77F5VRC","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:P77F5VRCGPAWDQRB4UVQXROM4K","target":"record","payload":{"canonical_record":{"source":{"id":"1302.6903","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-27T16:20:34Z","cross_cats_sorted":[],"title_canon_sha256":"49e6bc5f9ed993c591c38fcdc6cf11a2c8c36d187cd3b699e04579eb64bb17e5","abstract_canon_sha256":"ebdb1bf81dfc1ca43686f6fcbfc56112af07819ffd3116602dc2b8c78cdbf65c"},"schema_version":"1.0"},"canonical_sha256":"7ffe5ed62233c161c221e52b0bc5cce2a448468876ec70fb8106ec103d751427","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:18.218460Z","signature_b64":"gVnh2Mg5By99PD/xIe/jrLRo2sm9+/FY2lwK37wvquWQ708Js06DzmKx+nR09wG49nCM4Q7ForIIj6gL3kx9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ffe5ed62233c161c221e52b0bc5cce2a448468876ec70fb8106ec103d751427","last_reissued_at":"2026-05-18T03:32:18.217803Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:18.217803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.6903","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":"2026-05-18T03:32:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PCCo63j6shophNFbU9S0kPpH52qPc7pSs/nIP/frl+u5PukS74QWb5GLvvWxWE4wz7yb92hxWzCXOgCc5cN2Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:18:47.222351Z"},"content_sha256":"42941b2c417ec0ade6c319e52fc2562b03ade98136e9e8e4bb95f8a084f2f8f0","schema_version":"1.0","event_id":"sha256:42941b2c417ec0ade6c319e52fc2562b03ade98136e9e8e4bb95f8a084f2f8f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:P77F5VRCGPAWDQRB4UVQXROM4K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An extension of Nunokawa lemma and its example","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Hitoshi Shiraishi, Mamoru Nunokawa","submitted_at":"2013-02-27T16:20:34Z","abstract_excerpt":"For analytic functions p(z) in the open unit disk U with p(0)=1, Nunokwa has given a result which called Nunokawa lemma (Proc. Japan Acad., Ser. A 68 (1992)). By studying Nunokawa lemma, we obtain this expansion. In this paper, we introduce this result and its example."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6903","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":"2026-05-18T03:32:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ucoDaFlFkk7ttQ12qKAQYmAPPj77zNoEiWXCFpP6ipXUoo8YCPRj2cKIXLT4s7E3tC2zqpQuVY8RffrdaHthCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:18:47.222729Z"},"content_sha256":"7756cc83e51a7398e997a1102e1fd7d67448dacbf6e7cd448a1fe3210d42929b","schema_version":"1.0","event_id":"sha256:7756cc83e51a7398e997a1102e1fd7d67448dacbf6e7cd448a1fe3210d42929b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P77F5VRCGPAWDQRB4UVQXROM4K/bundle.json","state_url":"https://pith.science/pith/P77F5VRCGPAWDQRB4UVQXROM4K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P77F5VRCGPAWDQRB4UVQXROM4K/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":"2026-06-22T16:18:47Z","links":{"resolver":"https://pith.science/pith/P77F5VRCGPAWDQRB4UVQXROM4K","bundle":"https://pith.science/pith/P77F5VRCGPAWDQRB4UVQXROM4K/bundle.json","state":"https://pith.science/pith/P77F5VRCGPAWDQRB4UVQXROM4K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P77F5VRCGPAWDQRB4UVQXROM4K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:P77F5VRCGPAWDQRB4UVQXROM4K","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":"ebdb1bf81dfc1ca43686f6fcbfc56112af07819ffd3116602dc2b8c78cdbf65c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-27T16:20:34Z","title_canon_sha256":"49e6bc5f9ed993c591c38fcdc6cf11a2c8c36d187cd3b699e04579eb64bb17e5"},"schema_version":"1.0","source":{"id":"1302.6903","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6903","created_at":"2026-05-18T03:32:18Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6903v1","created_at":"2026-05-18T03:32:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6903","created_at":"2026-05-18T03:32:18Z"},{"alias_kind":"pith_short_12","alias_value":"P77F5VRCGPAW","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P77F5VRCGPAWDQRB","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P77F5VRC","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:7756cc83e51a7398e997a1102e1fd7d67448dacbf6e7cd448a1fe3210d42929b","target":"graph","created_at":"2026-05-18T03:32:18Z","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 p(z) in the open unit disk U with p(0)=1, Nunokwa has given a result which called Nunokawa lemma (Proc. Japan Acad., Ser. A 68 (1992)). By studying Nunokawa lemma, we obtain this expansion. In this paper, we introduce this result and its example.","authors_text":"Hitoshi Shiraishi, Mamoru Nunokawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-27T16:20:34Z","title":"An extension of Nunokawa lemma and its example"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6903","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":"sha256:42941b2c417ec0ade6c319e52fc2562b03ade98136e9e8e4bb95f8a084f2f8f0","target":"record","created_at":"2026-05-18T03:32:18Z","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":"ebdb1bf81dfc1ca43686f6fcbfc56112af07819ffd3116602dc2b8c78cdbf65c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-27T16:20:34Z","title_canon_sha256":"49e6bc5f9ed993c591c38fcdc6cf11a2c8c36d187cd3b699e04579eb64bb17e5"},"schema_version":"1.0","source":{"id":"1302.6903","kind":"arxiv","version":1}},"canonical_sha256":"7ffe5ed62233c161c221e52b0bc5cce2a448468876ec70fb8106ec103d751427","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ffe5ed62233c161c221e52b0bc5cce2a448468876ec70fb8106ec103d751427","first_computed_at":"2026-05-18T03:32:18.217803Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:18.217803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gVnh2Mg5By99PD/xIe/jrLRo2sm9+/FY2lwK37wvquWQ708Js06DzmKx+nR09wG49nCM4Q7ForIIj6gL3kx9CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:18.218460Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.6903","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42941b2c417ec0ade6c319e52fc2562b03ade98136e9e8e4bb95f8a084f2f8f0","sha256:7756cc83e51a7398e997a1102e1fd7d67448dacbf6e7cd448a1fe3210d42929b"],"state_sha256":"539e9c5a9e906437c357f3fb474ea838451f5b1d482f217d9a3770f3ea37de44"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k37W1cXIbZtoIJI+YnLlLpr+9WuP+5L6V+2RngCtPmSQJO2Pn81lzbGpd4x+nwAWViRwl2p3MZE1me4IjlnfCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:18:47.224796Z","bundle_sha256":"8d6e52d366a2b51b5c92377f26840122340441d3b736f17770796c1cade091af"}}