{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:ZRAZLXT4CBZCEFSU5QL3CTHLRI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a1e248eeeb3bbfaa2b910e656fb585222bed5f62b52905153563424f64bd9f5c","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2007-09-11T10:38:06Z","title_canon_sha256":"bb260ffc91a7132a6b5a594e5b25bb3e1b325bc66b1a9bdceca7580c52a231c0"},"schema_version":"1.0","source":{"id":"0709.1570","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0709.1570","created_at":"2026-05-18T03:50:00Z"},{"alias_kind":"arxiv_version","alias_value":"0709.1570v1","created_at":"2026-05-18T03:50:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.1570","created_at":"2026-05-18T03:50:00Z"},{"alias_kind":"pith_short_12","alias_value":"ZRAZLXT4CBZC","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"ZRAZLXT4CBZCEFSU","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"ZRAZLXT4","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:8963dd2e403c1bc3626478ee7d2f9e7e18d2b6d922a3dd9fabadf23a989eb695","target":"graph","created_at":"2026-05-18T03:50:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $\\Psi_n(x)$ be the monic polynomial having precisely all non-primitive $n$th roots of unity as its simple zeros. One has $\\Psi_n(x)=(x^n-1)/\\Phi_n(x)$, with $\\Phi_n(x)$ the $n$th cyclotomic polynomial. The coefficients of $\\Psi_n(x)$ are integers that like the coefficients of $\\Phi_n(x)$ tend to be surprisingly small in absolute value, e.g. for $n<561$ all coefficients of $\\Psi_n(x)$ are $\\le 1$ in absolute value. We establish various properties of the coefficients of $\\Psi_n(x)$.","authors_text":"Pieter Moree","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2007-09-11T10:38:06Z","title":"Reciprocal cyclotomic polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.1570","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a103176d7a4e061a9048d747cfde63025cc4851919a657e8d57cf585f8cb7080","target":"record","created_at":"2026-05-18T03:50:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a1e248eeeb3bbfaa2b910e656fb585222bed5f62b52905153563424f64bd9f5c","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2007-09-11T10:38:06Z","title_canon_sha256":"bb260ffc91a7132a6b5a594e5b25bb3e1b325bc66b1a9bdceca7580c52a231c0"},"schema_version":"1.0","source":{"id":"0709.1570","kind":"arxiv","version":1}},"canonical_sha256":"cc4195de7c1072221654ec17b14ceb8a105928b68e8e60140965d3f2009ae1c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc4195de7c1072221654ec17b14ceb8a105928b68e8e60140965d3f2009ae1c3","first_computed_at":"2026-05-18T03:50:00.232871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:00.232871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X7jc2LssPV0hfpiu/HWdC7/oPBopi+tu1QDlt17pnko+YkqPRTMdfyJTyk5+oc2ViKPkDvKc3d3ehlEeUeyFBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:00.233379Z","signed_message":"canonical_sha256_bytes"},"source_id":"0709.1570","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a103176d7a4e061a9048d747cfde63025cc4851919a657e8d57cf585f8cb7080","sha256:8963dd2e403c1bc3626478ee7d2f9e7e18d2b6d922a3dd9fabadf23a989eb695"],"state_sha256":"9f20abb83e8405d108a115999c4ac485e21e180ccfe4c8d999be4c4fa0b2e734"}