{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:P5Y3T5YP2XGI357ZT22J6MGWRX","short_pith_number":"pith:P5Y3T5YP","schema_version":"1.0","canonical_sha256":"7f71b9f70fd5cc8df7f99eb49f30d68dccba6e5b875fde63dcd851f3ef5664cf","source":{"kind":"arxiv","id":"1801.01369","version":1},"attestation_state":"computed","paper":{"title":"Fibonacci Numbers and the Golden Ratio in Biology, Physics, Astrophysics, Chemistry and Technology: A Non-Exhaustive Review","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.pop-ph","authors_text":"Vladimir Pletser","submitted_at":"2017-12-29T03:10:47Z","abstract_excerpt":"Fibonacci numbers and the golden ratio can be found in nearly all domains of Science, appearing when self-organization processes are at play and/or expressing minimum energy configurations. Several non-exhaustive examples are given in biology (natural and artificial phyllotaxis, genetic code and DNA), physics (hydrogen bonds, chaos, superconductivity), astrophysics (pulsating stars, black holes), chemistry (quasicrystals, protein AB models), and technology (tribology, resistors, quantum computing, quantum phase transitions, photonics)."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1801.01369","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.pop-ph","submitted_at":"2017-12-29T03:10:47Z","cross_cats_sorted":[],"title_canon_sha256":"9da80500c7cfde4fe336f4dc6e82c5c84739bd5c8366487d855fd6a4a89995cb","abstract_canon_sha256":"78e9bcb79f57cb9ae3bf0e3f21448edfdcd6d9481acee63692708686d4377d05"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:42.326996Z","signature_b64":"t/XX8krLpDk9nLW9EHG9uyF/P1iT1t2K5mznojP1rQmfSIj1f1SADDS0V99qOARnomF7/j6F6Xjke9JTTX9rDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f71b9f70fd5cc8df7f99eb49f30d68dccba6e5b875fde63dcd851f3ef5664cf","last_reissued_at":"2026-05-18T00:26:42.326430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:42.326430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fibonacci Numbers and the Golden Ratio in Biology, Physics, Astrophysics, Chemistry and Technology: A Non-Exhaustive Review","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.pop-ph","authors_text":"Vladimir Pletser","submitted_at":"2017-12-29T03:10:47Z","abstract_excerpt":"Fibonacci numbers and the golden ratio can be found in nearly all domains of Science, appearing when self-organization processes are at play and/or expressing minimum energy configurations. Several non-exhaustive examples are given in biology (natural and artificial phyllotaxis, genetic code and DNA), physics (hydrogen bonds, chaos, superconductivity), astrophysics (pulsating stars, black holes), chemistry (quasicrystals, protein AB models), and technology (tribology, resistors, quantum computing, quantum phase transitions, photonics)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01369","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1801.01369","created_at":"2026-05-18T00:26:42.326510+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.01369v1","created_at":"2026-05-18T00:26:42.326510+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.01369","created_at":"2026-05-18T00:26:42.326510+00:00"},{"alias_kind":"pith_short_12","alias_value":"P5Y3T5YP2XGI","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"P5Y3T5YP2XGI357Z","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"P5Y3T5YP","created_at":"2026-05-18T12:31:37.085036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/P5Y3T5YP2XGI357ZT22J6MGWRX","json":"https://pith.science/pith/P5Y3T5YP2XGI357ZT22J6MGWRX.json","graph_json":"https://pith.science/api/pith-number/P5Y3T5YP2XGI357ZT22J6MGWRX/graph.json","events_json":"https://pith.science/api/pith-number/P5Y3T5YP2XGI357ZT22J6MGWRX/events.json","paper":"https://pith.science/paper/P5Y3T5YP"},"agent_actions":{"view_html":"https://pith.science/pith/P5Y3T5YP2XGI357ZT22J6MGWRX","download_json":"https://pith.science/pith/P5Y3T5YP2XGI357ZT22J6MGWRX.json","view_paper":"https://pith.science/paper/P5Y3T5YP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.01369&json=true","fetch_graph":"https://pith.science/api/pith-number/P5Y3T5YP2XGI357ZT22J6MGWRX/graph.json","fetch_events":"https://pith.science/api/pith-number/P5Y3T5YP2XGI357ZT22J6MGWRX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P5Y3T5YP2XGI357ZT22J6MGWRX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P5Y3T5YP2XGI357ZT22J6MGWRX/action/storage_attestation","attest_author":"https://pith.science/pith/P5Y3T5YP2XGI357ZT22J6MGWRX/action/author_attestation","sign_citation":"https://pith.science/pith/P5Y3T5YP2XGI357ZT22J6MGWRX/action/citation_signature","submit_replication":"https://pith.science/pith/P5Y3T5YP2XGI357ZT22J6MGWRX/action/replication_record"}},"created_at":"2026-05-18T00:26:42.326510+00:00","updated_at":"2026-05-18T00:26:42.326510+00:00"}