{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:RKTG6AVE6ZX46XGSLDZXLJXNDG","short_pith_number":"pith:RKTG6AVE","schema_version":"1.0","canonical_sha256":"8aa66f02a4f66fcf5cd258f375a6ed19aee65c20475c57e1a08c229dfa3d324f","source":{"kind":"arxiv","id":"1501.05830","version":1},"attestation_state":"computed","paper":{"title":"A $q$-analogue of the Biperiodic Fibonacci Sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jos\\'e L. Ram\\'irez, V\\'ictor Sirvent","submitted_at":"2015-01-23T15:27:49Z","abstract_excerpt":"The Fibonacci sequence has been generalized in many ways. One of them is defined by the relation $t_n=at_{n-1}+t_{n-2}$ if $n$ is even, $t_n=bt_{n-1}+t_{n-2}$ if $n$ is odd, with initial values $t_0=0$ and $t_1=1$, where $a$ and $b$ are positive integers. This sequence is called biperiodic Fibonacci sequence. In this paper, we introduce a $q$-analogue of this sequence. We prove several identities of $q$-analogues of the Fibonacci sequence. We give algebraic and combinatorial proofs."},"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":"1501.05830","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-23T15:27:49Z","cross_cats_sorted":[],"title_canon_sha256":"7a85c207fefe1a8e22d04464f82a125c8a398bcb351753069eea29ba5f4e1672","abstract_canon_sha256":"93107e9ce8a3639f40a629b9753026dc7980595a578943a7d54d3c4d0266c156"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:48.871139Z","signature_b64":"9wZRFdVAgzIxh42AtAI150EhLO6qzimad6c6qvonu9PUs9x1iTZLFrhiEh1dyCqXorKQJUE5+I0/IgW69AAeAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8aa66f02a4f66fcf5cd258f375a6ed19aee65c20475c57e1a08c229dfa3d324f","last_reissued_at":"2026-05-18T02:28:48.870791Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:48.870791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A $q$-analogue of the Biperiodic Fibonacci Sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jos\\'e L. Ram\\'irez, V\\'ictor Sirvent","submitted_at":"2015-01-23T15:27:49Z","abstract_excerpt":"The Fibonacci sequence has been generalized in many ways. One of them is defined by the relation $t_n=at_{n-1}+t_{n-2}$ if $n$ is even, $t_n=bt_{n-1}+t_{n-2}$ if $n$ is odd, with initial values $t_0=0$ and $t_1=1$, where $a$ and $b$ are positive integers. This sequence is called biperiodic Fibonacci sequence. In this paper, we introduce a $q$-analogue of this sequence. We prove several identities of $q$-analogues of the Fibonacci sequence. We give algebraic and combinatorial proofs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05830","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":"1501.05830","created_at":"2026-05-18T02:28:48.870847+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.05830v1","created_at":"2026-05-18T02:28:48.870847+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05830","created_at":"2026-05-18T02:28:48.870847+00:00"},{"alias_kind":"pith_short_12","alias_value":"RKTG6AVE6ZX4","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"RKTG6AVE6ZX46XGS","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"RKTG6AVE","created_at":"2026-05-18T12:29:39.896362+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/RKTG6AVE6ZX46XGSLDZXLJXNDG","json":"https://pith.science/pith/RKTG6AVE6ZX46XGSLDZXLJXNDG.json","graph_json":"https://pith.science/api/pith-number/RKTG6AVE6ZX46XGSLDZXLJXNDG/graph.json","events_json":"https://pith.science/api/pith-number/RKTG6AVE6ZX46XGSLDZXLJXNDG/events.json","paper":"https://pith.science/paper/RKTG6AVE"},"agent_actions":{"view_html":"https://pith.science/pith/RKTG6AVE6ZX46XGSLDZXLJXNDG","download_json":"https://pith.science/pith/RKTG6AVE6ZX46XGSLDZXLJXNDG.json","view_paper":"https://pith.science/paper/RKTG6AVE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.05830&json=true","fetch_graph":"https://pith.science/api/pith-number/RKTG6AVE6ZX46XGSLDZXLJXNDG/graph.json","fetch_events":"https://pith.science/api/pith-number/RKTG6AVE6ZX46XGSLDZXLJXNDG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RKTG6AVE6ZX46XGSLDZXLJXNDG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RKTG6AVE6ZX46XGSLDZXLJXNDG/action/storage_attestation","attest_author":"https://pith.science/pith/RKTG6AVE6ZX46XGSLDZXLJXNDG/action/author_attestation","sign_citation":"https://pith.science/pith/RKTG6AVE6ZX46XGSLDZXLJXNDG/action/citation_signature","submit_replication":"https://pith.science/pith/RKTG6AVE6ZX46XGSLDZXLJXNDG/action/replication_record"}},"created_at":"2026-05-18T02:28:48.870847+00:00","updated_at":"2026-05-18T02:28:48.870847+00:00"}