{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QZG65VCI7OZ2P6VNJNKEWQJLNT","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":"845f37aed3589822f93a161b51a923a8321642e52024a49c17edf9f2d11f752a","cross_cats_sorted":["math.HO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-16T20:53:54Z","title_canon_sha256":"2a659c651a4056050abf98fd93823d5e1a1aa49a6899c58b6b4c5d67af3b41cf"},"schema_version":"1.0","source":{"id":"1707.04944","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.04944","created_at":"2026-05-18T00:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"1707.04944v1","created_at":"2026-05-18T00:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04944","created_at":"2026-05-18T00:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"QZG65VCI7OZ2","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QZG65VCI7OZ2P6VN","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QZG65VCI","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:b5d8403ccc7672f9fb4ab6968193eb556946002a35367f67757fa58efcc09654","target":"graph","created_at":"2026-05-18T00:40:11Z","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":"The link between the equation $b(b+a)-a^2=0$ concerning the side $b$ and the diagonal $a$ of a regular pentagon and the {\\it Cassini identity} $F_{i}F_{i+2}-F_{i+1}^2=(-1)^{i}$, concerning three consecutive Fibonacci numbers, is very strong. In this paper we present our thesis that the two mentioned equations were \"almost simultaneously\" discovered by the {\\it Pythagorean School}.","authors_text":"Giuseppe Pirillo","cross_cats":["math.HO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-16T20:53:54Z","title":"A characterization of Fibonacci numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04944","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":"sha256:87ef5fa4f45dd46d61dab4aa354476149c5f6b7a63622acbf083634ddf8cf386","target":"record","created_at":"2026-05-18T00:40:11Z","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":"845f37aed3589822f93a161b51a923a8321642e52024a49c17edf9f2d11f752a","cross_cats_sorted":["math.HO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-07-16T20:53:54Z","title_canon_sha256":"2a659c651a4056050abf98fd93823d5e1a1aa49a6899c58b6b4c5d67af3b41cf"},"schema_version":"1.0","source":{"id":"1707.04944","kind":"arxiv","version":1}},"canonical_sha256":"864deed448fbb3a7faad4b544b412b6cea4366c0a9f59f6b19dc562d8e589c41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"864deed448fbb3a7faad4b544b412b6cea4366c0a9f59f6b19dc562d8e589c41","first_computed_at":"2026-05-18T00:40:11.738081Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:11.738081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+1xHxAVQrArJ/fw+aWhObNJT8Bmh+6pr2VPzpe64m5adJHvt6vBSI/XxJCbHkESDd7DCRpOGP0KzxUE5yWNuBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:11.738658Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.04944","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87ef5fa4f45dd46d61dab4aa354476149c5f6b7a63622acbf083634ddf8cf386","sha256:b5d8403ccc7672f9fb4ab6968193eb556946002a35367f67757fa58efcc09654"],"state_sha256":"5fdd8e1a4180d91efaf72ffb1bd98ac98a7307a971cda1ea917eb2b864207746"}