{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:W2HRGFOM5CB5HND5P6VNL5STBG","short_pith_number":"pith:W2HRGFOM","schema_version":"1.0","canonical_sha256":"b68f1315cce883d3b47d7faad5f653098cf31155b4350b98931725e51a4c8a7a","source":{"kind":"arxiv","id":"1909.01938","version":1},"attestation_state":"computed","paper":{"title":"The Fibonacci Quilt Game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Alexandra Newlon, Steven J. Miller","submitted_at":"2019-09-04T16:55:33Z","abstract_excerpt":"Zeckendorf proved that every positive integer can be expressed as the sum of non-consecutive Fibonacci numbers. This theorem inspired a beautiful game, the Zeckendorf Game. Two players begin with $n \\ 1$'s and take turns applying rules inspired by the Fibonacci recurrence, $F_{n+1} = F_n + F_{n-1}$, until a decomposition without consecutive terms is reached; whoever makes the last move wins. We look at a game resulting from a generalization of the Fibonacci numbers, the Fibonacci Quilt sequence. These arise from the two-dimensional geometric property of tiling the plane through the Fibonacci s"},"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":"1909.01938","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-09-04T16:55:33Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"5957cd9f8f52d4d6572b6995187f98ad30665432731e74f595e7710567906342","abstract_canon_sha256":"4884e6e8c9c052f46f4afcc0eb481dd0e74f2c25f0230869104d6430ed72d031"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:02:21.944099Z","signature_b64":"LmCf65x+7saeeYkyv8P7tWwaojE6PONuycHYb248MqwTBd1/UP5OrGciTdVYQv3/vUDaSqKlNc0rlTlz2YebDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b68f1315cce883d3b47d7faad5f653098cf31155b4350b98931725e51a4c8a7a","last_reissued_at":"2026-07-05T00:02:21.943713Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:02:21.943713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Fibonacci Quilt Game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Alexandra Newlon, Steven J. Miller","submitted_at":"2019-09-04T16:55:33Z","abstract_excerpt":"Zeckendorf proved that every positive integer can be expressed as the sum of non-consecutive Fibonacci numbers. This theorem inspired a beautiful game, the Zeckendorf Game. Two players begin with $n \\ 1$'s and take turns applying rules inspired by the Fibonacci recurrence, $F_{n+1} = F_n + F_{n-1}$, until a decomposition without consecutive terms is reached; whoever makes the last move wins. We look at a game resulting from a generalization of the Fibonacci numbers, the Fibonacci Quilt sequence. These arise from the two-dimensional geometric property of tiling the plane through the Fibonacci s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.01938","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/1909.01938/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":"1909.01938","created_at":"2026-07-05T00:02:21.943766+00:00"},{"alias_kind":"arxiv_version","alias_value":"1909.01938v1","created_at":"2026-07-05T00:02:21.943766+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.01938","created_at":"2026-07-05T00:02:21.943766+00:00"},{"alias_kind":"pith_short_12","alias_value":"W2HRGFOM5CB5","created_at":"2026-07-05T00:02:21.943766+00:00"},{"alias_kind":"pith_short_16","alias_value":"W2HRGFOM5CB5HND5","created_at":"2026-07-05T00:02:21.943766+00:00"},{"alias_kind":"pith_short_8","alias_value":"W2HRGFOM","created_at":"2026-07-05T00:02:21.943766+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/W2HRGFOM5CB5HND5P6VNL5STBG","json":"https://pith.science/pith/W2HRGFOM5CB5HND5P6VNL5STBG.json","graph_json":"https://pith.science/api/pith-number/W2HRGFOM5CB5HND5P6VNL5STBG/graph.json","events_json":"https://pith.science/api/pith-number/W2HRGFOM5CB5HND5P6VNL5STBG/events.json","paper":"https://pith.science/paper/W2HRGFOM"},"agent_actions":{"view_html":"https://pith.science/pith/W2HRGFOM5CB5HND5P6VNL5STBG","download_json":"https://pith.science/pith/W2HRGFOM5CB5HND5P6VNL5STBG.json","view_paper":"https://pith.science/paper/W2HRGFOM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1909.01938&json=true","fetch_graph":"https://pith.science/api/pith-number/W2HRGFOM5CB5HND5P6VNL5STBG/graph.json","fetch_events":"https://pith.science/api/pith-number/W2HRGFOM5CB5HND5P6VNL5STBG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W2HRGFOM5CB5HND5P6VNL5STBG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W2HRGFOM5CB5HND5P6VNL5STBG/action/storage_attestation","attest_author":"https://pith.science/pith/W2HRGFOM5CB5HND5P6VNL5STBG/action/author_attestation","sign_citation":"https://pith.science/pith/W2HRGFOM5CB5HND5P6VNL5STBG/action/citation_signature","submit_replication":"https://pith.science/pith/W2HRGFOM5CB5HND5P6VNL5STBG/action/replication_record"}},"created_at":"2026-07-05T00:02:21.943766+00:00","updated_at":"2026-07-05T00:02:21.943766+00:00"}