{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3GMZYKTLA7FLGUO264YROOK7O3","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":"a0576a40c7c297f3453741a260e0815f2cb5e969d5d2d18bd64bac251b29d0f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-20T03:22:59Z","title_canon_sha256":"0a2e27bc77c418bf8a1bc0ecbcdb026146a91c600c5d2ab00dfa4663140516ff"},"schema_version":"1.0","source":{"id":"1601.05160","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05160","created_at":"2026-05-18T01:21:36Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05160v3","created_at":"2026-05-18T01:21:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05160","created_at":"2026-05-18T01:21:36Z"},{"alias_kind":"pith_short_12","alias_value":"3GMZYKTLA7FL","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3GMZYKTLA7FLGUO2","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3GMZYKTL","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:e8e46062d21fa7e7721ca58b7d40707501aa97f6b93d6b85555fbc0bd209d2ed","target":"graph","created_at":"2026-05-18T01:21:36Z","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":"Based on the structure of Fibonacci sequence, we give a new proof for the irrationality exponents of the Fibonacci real numbers. Moreover, we obtain all the irrationality exponents of the real numbers corresponding to the differences of Fibonacci sequence.","authors_text":"Jie-Meng Zhang, Ying-jun Guo, Zhi-xiong Wen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-20T03:22:59Z","title":"On the rational approximations to the real numbers corresponding to the differences of the Fibonacci sequence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05160","kind":"arxiv","version":3},"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":"sha256:17522f669b3e470e910235313ee82ff25fae0810ab52d161f36880cae9e89595","target":"record","created_at":"2026-05-18T01:21:36Z","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":"a0576a40c7c297f3453741a260e0815f2cb5e969d5d2d18bd64bac251b29d0f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-20T03:22:59Z","title_canon_sha256":"0a2e27bc77c418bf8a1bc0ecbcdb026146a91c600c5d2ab00dfa4663140516ff"},"schema_version":"1.0","source":{"id":"1601.05160","kind":"arxiv","version":3}},"canonical_sha256":"d9999c2a6b07cab351daf73117395f76d4e89ee15b17f44d7a46aa279940c2f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9999c2a6b07cab351daf73117395f76d4e89ee15b17f44d7a46aa279940c2f1","first_computed_at":"2026-05-18T01:21:36.574156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:36.574156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+CFr0x6nXujKfLhyjR9BrE8u0BPVRmfJacYmsSmMf2C4zOrN9FxL2JiskYYNSlsn4S64cb31vWrHyuUecoPyDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:36.574567Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05160","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17522f669b3e470e910235313ee82ff25fae0810ab52d161f36880cae9e89595","sha256:e8e46062d21fa7e7721ca58b7d40707501aa97f6b93d6b85555fbc0bd209d2ed"],"state_sha256":"6564f8b781a0161c90a8360247d3553079ddf9ca05136c1cc03c9c94865abd88"}