{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:NGDZOKMZMS45PYG5QS6SSZCHFH","short_pith_number":"pith:NGDZOKMZ","schema_version":"1.0","canonical_sha256":"698797299964b9d7e0dd84bd29644729db0b9880ab5b162eab846225fd44e34e","source":{"kind":"arxiv","id":"1101.4255","version":1},"attestation_state":"computed","paper":{"title":"Maximum Gap in (Inverse) Cyclotomic Polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Cheol-Min Park, Eunjeong Lee, Hoon Hong, Hyang-Sook Lee","submitted_at":"2011-01-22T03:02:01Z","abstract_excerpt":"Let $g(f)$ denote the maximum of the differences (gaps) between two consecutive exponents occurring in a polynomial $f$. Let $\\Phi_n$ denote the $n$-th cyclotomic polynomial and let $\\Psi_n$ denote the $n$-th inverse cyclotomic polynomial. In this note, we study $g(\\Phi_n)$ and $g(\\Psi_n)$ where $n$ is a product of odd primes, say $p_1 < p_2 < p_3$, etc. It is trivial to determine $g(\\Phi_{p_1})$, $g(\\Psi_{p_1})$ and $g(\\Psi_{p_1p_2})$. Hence the simplest non-trivial cases are $g(\\Phi_{p_1p_2})$ and $g(\\Psi_{p_1p_2p_3})$. We provide an exact expression for $g(\\Phi_{p_1p_2}).$ We also provide a"},"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":"1101.4255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-01-22T03:02:01Z","cross_cats_sorted":[],"title_canon_sha256":"9fc11e927b1de2d5e2ed8241827b3e085ee06330ea2b7688760d45e1e9c2801c","abstract_canon_sha256":"ebfbd86bf25239e1b10c11923c98337d032ee459f7e7977190bb32e34e13abb3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:11.257145Z","signature_b64":"UzZYgRCznWwJ6SpVav8JvwnopNONVc8Lo2XM+5I38hy+yjHraYh7m9DHpsN+V8SBLDOQUaKK6C75ktlNJ0f+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"698797299964b9d7e0dd84bd29644729db0b9880ab5b162eab846225fd44e34e","last_reissued_at":"2026-05-18T04:31:11.256668Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:11.256668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximum Gap in (Inverse) Cyclotomic Polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Cheol-Min Park, Eunjeong Lee, Hoon Hong, Hyang-Sook Lee","submitted_at":"2011-01-22T03:02:01Z","abstract_excerpt":"Let $g(f)$ denote the maximum of the differences (gaps) between two consecutive exponents occurring in a polynomial $f$. Let $\\Phi_n$ denote the $n$-th cyclotomic polynomial and let $\\Psi_n$ denote the $n$-th inverse cyclotomic polynomial. In this note, we study $g(\\Phi_n)$ and $g(\\Psi_n)$ where $n$ is a product of odd primes, say $p_1 < p_2 < p_3$, etc. It is trivial to determine $g(\\Phi_{p_1})$, $g(\\Psi_{p_1})$ and $g(\\Psi_{p_1p_2})$. Hence the simplest non-trivial cases are $g(\\Phi_{p_1p_2})$ and $g(\\Psi_{p_1p_2p_3})$. We provide an exact expression for $g(\\Phi_{p_1p_2}).$ We also provide a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4255","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":"1101.4255","created_at":"2026-05-18T04:31:11.256745+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.4255v1","created_at":"2026-05-18T04:31:11.256745+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4255","created_at":"2026-05-18T04:31:11.256745+00:00"},{"alias_kind":"pith_short_12","alias_value":"NGDZOKMZMS45","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"NGDZOKMZMS45PYG5","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"NGDZOKMZ","created_at":"2026-05-18T12:26:37.096874+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/NGDZOKMZMS45PYG5QS6SSZCHFH","json":"https://pith.science/pith/NGDZOKMZMS45PYG5QS6SSZCHFH.json","graph_json":"https://pith.science/api/pith-number/NGDZOKMZMS45PYG5QS6SSZCHFH/graph.json","events_json":"https://pith.science/api/pith-number/NGDZOKMZMS45PYG5QS6SSZCHFH/events.json","paper":"https://pith.science/paper/NGDZOKMZ"},"agent_actions":{"view_html":"https://pith.science/pith/NGDZOKMZMS45PYG5QS6SSZCHFH","download_json":"https://pith.science/pith/NGDZOKMZMS45PYG5QS6SSZCHFH.json","view_paper":"https://pith.science/paper/NGDZOKMZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.4255&json=true","fetch_graph":"https://pith.science/api/pith-number/NGDZOKMZMS45PYG5QS6SSZCHFH/graph.json","fetch_events":"https://pith.science/api/pith-number/NGDZOKMZMS45PYG5QS6SSZCHFH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NGDZOKMZMS45PYG5QS6SSZCHFH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NGDZOKMZMS45PYG5QS6SSZCHFH/action/storage_attestation","attest_author":"https://pith.science/pith/NGDZOKMZMS45PYG5QS6SSZCHFH/action/author_attestation","sign_citation":"https://pith.science/pith/NGDZOKMZMS45PYG5QS6SSZCHFH/action/citation_signature","submit_replication":"https://pith.science/pith/NGDZOKMZMS45PYG5QS6SSZCHFH/action/replication_record"}},"created_at":"2026-05-18T04:31:11.256745+00:00","updated_at":"2026-05-18T04:31:11.256745+00:00"}