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Specifically, if we put $$\\epsilon(j)=\\begin{cases}(-1)^k, & \\text{if }j=F_k\\text{ for some }k\\\\ 0, & \\text{in other case}\\end{cases},$$ where $F_k$ is the $k$-th Fibonacci number, then we define the general terms of the lower and upper Wythoff-Fibonacci sequences by $$LWF(n)=\\begin{cases} 1, & \\text{if }n=1,\\\\ 3, & \\text{if }n=2,\\\\ a(n)+\\epsilon(n), & \\text{if }n\\geq 3.\\end{cases}$$ and $$UWF(n)=\\begin{cases} 2, & \\text{if }n=1,\\\\ b(n)+\\epsilon(n), & \\text{if "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.00814","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-01T11:40:48Z","cross_cats_sorted":[],"title_canon_sha256":"8622a5cd525004ac8139c18bba583a51411fa5bf1563469d4243c45f4ce89741","abstract_canon_sha256":"76e9604e618936ebf48258ae1a11a2e7022e28be124c7cff8ea98cfd531d91df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T01:17:56.119230Z","signature_b64":"XVYnrKpyt+JJuq7iKuslw7vBUnr6DqXuPsb/3iSg8goQaV1lePIaNX9eFwL93K6j6dhYbNmjqNdRkNF7MNy9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e36ab662119f5b29368bfee68f6d8d52524a3e2437bbbe7daab17a075e47314","last_reissued_at":"2026-07-02T01:17:56.118741Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T01:17:56.118741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wythoff-Fibonacci Sequences and a Perturbed Greedy Almost-involution","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Iker Malaina, Luis Mart\\'inez","submitted_at":"2026-07-01T11:40:48Z","abstract_excerpt":"We introduce the lower and upper Wythoff-Fibonacci sequences, obtained from the classical Wythoff sequences by a Fibonacci correction. Specifically, if we put $$\\epsilon(j)=\\begin{cases}(-1)^k, & \\text{if }j=F_k\\text{ for some }k\\\\ 0, & \\text{in other case}\\end{cases},$$ where $F_k$ is the $k$-th Fibonacci number, then we define the general terms of the lower and upper Wythoff-Fibonacci sequences by $$LWF(n)=\\begin{cases} 1, & \\text{if }n=1,\\\\ 3, & \\text{if }n=2,\\\\ a(n)+\\epsilon(n), & \\text{if }n\\geq 3.\\end{cases}$$ and $$UWF(n)=\\begin{cases} 2, & \\text{if }n=1,\\\\ b(n)+\\epsilon(n), & \\text{if "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00814","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.00814/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2607.00814","created_at":"2026-07-02T01:17:56.118803+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.00814v1","created_at":"2026-07-02T01:17:56.118803+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00814","created_at":"2026-07-02T01:17:56.118803+00:00"},{"alias_kind":"pith_short_12","alias_value":"BY3KWZRBDH23","created_at":"2026-07-02T01:17:56.118803+00:00"},{"alias_kind":"pith_short_16","alias_value":"BY3KWZRBDH23FE3I","created_at":"2026-07-02T01:17:56.118803+00:00"},{"alias_kind":"pith_short_8","alias_value":"BY3KWZRB","created_at":"2026-07-02T01:17:56.118803+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/BY3KWZRBDH23FE3IX7XGR5WY2U","json":"https://pith.science/pith/BY3KWZRBDH23FE3IX7XGR5WY2U.json","graph_json":"https://pith.science/api/pith-number/BY3KWZRBDH23FE3IX7XGR5WY2U/graph.json","events_json":"https://pith.science/api/pith-number/BY3KWZRBDH23FE3IX7XGR5WY2U/events.json","paper":"https://pith.science/paper/BY3KWZRB"},"agent_actions":{"view_html":"https://pith.science/pith/BY3KWZRBDH23FE3IX7XGR5WY2U","download_json":"https://pith.science/pith/BY3KWZRBDH23FE3IX7XGR5WY2U.json","view_paper":"https://pith.science/paper/BY3KWZRB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.00814&json=true","fetch_graph":"https://pith.science/api/pith-number/BY3KWZRBDH23FE3IX7XGR5WY2U/graph.json","fetch_events":"https://pith.science/api/pith-number/BY3KWZRBDH23FE3IX7XGR5WY2U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BY3KWZRBDH23FE3IX7XGR5WY2U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BY3KWZRBDH23FE3IX7XGR5WY2U/action/storage_attestation","attest_author":"https://pith.science/pith/BY3KWZRBDH23FE3IX7XGR5WY2U/action/author_attestation","sign_citation":"https://pith.science/pith/BY3KWZRBDH23FE3IX7XGR5WY2U/action/citation_signature","submit_replication":"https://pith.science/pith/BY3KWZRBDH23FE3IX7XGR5WY2U/action/replication_record"}},"created_at":"2026-07-02T01:17:56.118803+00:00","updated_at":"2026-07-02T01:17:56.118803+00:00"}