{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:BDJV33WEHVTBUF5OVJQCRXRJYF","short_pith_number":"pith:BDJV33WE","schema_version":"1.0","canonical_sha256":"08d35deec43d661a17aeaa6028de29c1699f08ae950e40f3898e7b8117e64c41","source":{"kind":"arxiv","id":"1508.07531","version":3},"attestation_state":"computed","paper":{"title":"A Generalization of Zeckendorf's Theorem via Circumscribed $m$-gons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eva Fourakis, Eyvindur A. Palsson, Hannah Paugh, Pamela E. Harris, Pari L. Ford, Robert Dorward, Steven J. Miller","submitted_at":"2015-08-30T05:50:13Z","abstract_excerpt":"Zeckendorf's theorem states that every positive integer can be uniquely decomposed as a sum of nonconsecutive Fibonacci numbers, where the Fibonacci numbers satisfy $F_n=F_{n-1}+F_{n-2}$ for $n\\geq 3$, $F_1=1$ and $F_2=2$. The distribution of the number of summands in such decomposition converges to a Gaussian, the gaps between summands converges to geometric decay, and the distribution of the longest gap is similar to that of the longest run of heads in a biased coin; these results also hold more generally, though for technical reasons previous work needed to assume the coefficients in the re"},"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":"1508.07531","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-30T05:50:13Z","cross_cats_sorted":[],"title_canon_sha256":"f3a16aee78181a835e81b90783fa86a997f0908d4d851b007b74e9d37044b690","abstract_canon_sha256":"3fd8dedc447c72ee2eb38bbfdc6527aa684d49b0b22b645eed735dbbf2e58423"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:29.122358Z","signature_b64":"SvNduSYyVU6PXUaWNSErsPnqIa0P8RgUKZdY2641uxWHfK74g3lgHNhygchcwNjsYHgGWDiYN8phuqxCr6cHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08d35deec43d661a17aeaa6028de29c1699f08ae950e40f3898e7b8117e64c41","last_reissued_at":"2026-05-18T01:01:29.121931Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:29.121931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Generalization of Zeckendorf's Theorem via Circumscribed $m$-gons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Eva Fourakis, Eyvindur A. Palsson, Hannah Paugh, Pamela E. Harris, Pari L. Ford, Robert Dorward, Steven J. Miller","submitted_at":"2015-08-30T05:50:13Z","abstract_excerpt":"Zeckendorf's theorem states that every positive integer can be uniquely decomposed as a sum of nonconsecutive Fibonacci numbers, where the Fibonacci numbers satisfy $F_n=F_{n-1}+F_{n-2}$ for $n\\geq 3$, $F_1=1$ and $F_2=2$. The distribution of the number of summands in such decomposition converges to a Gaussian, the gaps between summands converges to geometric decay, and the distribution of the longest gap is similar to that of the longest run of heads in a biased coin; these results also hold more generally, though for technical reasons previous work needed to assume the coefficients in the re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07531","kind":"arxiv","version":3},"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":"1508.07531","created_at":"2026-05-18T01:01:29.121986+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.07531v3","created_at":"2026-05-18T01:01:29.121986+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07531","created_at":"2026-05-18T01:01:29.121986+00:00"},{"alias_kind":"pith_short_12","alias_value":"BDJV33WEHVTB","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BDJV33WEHVTBUF5O","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BDJV33WE","created_at":"2026-05-18T12:29:14.074870+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/BDJV33WEHVTBUF5OVJQCRXRJYF","json":"https://pith.science/pith/BDJV33WEHVTBUF5OVJQCRXRJYF.json","graph_json":"https://pith.science/api/pith-number/BDJV33WEHVTBUF5OVJQCRXRJYF/graph.json","events_json":"https://pith.science/api/pith-number/BDJV33WEHVTBUF5OVJQCRXRJYF/events.json","paper":"https://pith.science/paper/BDJV33WE"},"agent_actions":{"view_html":"https://pith.science/pith/BDJV33WEHVTBUF5OVJQCRXRJYF","download_json":"https://pith.science/pith/BDJV33WEHVTBUF5OVJQCRXRJYF.json","view_paper":"https://pith.science/paper/BDJV33WE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.07531&json=true","fetch_graph":"https://pith.science/api/pith-number/BDJV33WEHVTBUF5OVJQCRXRJYF/graph.json","fetch_events":"https://pith.science/api/pith-number/BDJV33WEHVTBUF5OVJQCRXRJYF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BDJV33WEHVTBUF5OVJQCRXRJYF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BDJV33WEHVTBUF5OVJQCRXRJYF/action/storage_attestation","attest_author":"https://pith.science/pith/BDJV33WEHVTBUF5OVJQCRXRJYF/action/author_attestation","sign_citation":"https://pith.science/pith/BDJV33WEHVTBUF5OVJQCRXRJYF/action/citation_signature","submit_replication":"https://pith.science/pith/BDJV33WEHVTBUF5OVJQCRXRJYF/action/replication_record"}},"created_at":"2026-05-18T01:01:29.121986+00:00","updated_at":"2026-05-18T01:01:29.121986+00:00"}