{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5J3LD2PWI2M7Y5B3NFDLNNZNPT","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":"60cca542999091d789be93675a28d8ca8fc31827e1651a8be8dc0d8d09462ba2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-31T07:49:11Z","title_canon_sha256":"9134077e7e486a18260cb4dbf5d789efa54c6af6e0d8c62aafa12f2c44013fb4"},"schema_version":"1.0","source":{"id":"1807.11693","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.11693","created_at":"2026-05-18T00:09:21Z"},{"alias_kind":"arxiv_version","alias_value":"1807.11693v1","created_at":"2026-05-18T00:09:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11693","created_at":"2026-05-18T00:09:21Z"},{"alias_kind":"pith_short_12","alias_value":"5J3LD2PWI2M7","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5J3LD2PWI2M7Y5B3","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5J3LD2PW","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:4987321b10ed3f0a4ceebdb5e4aba7895a906aee72ecab5ef9df2e39fd556659","target":"graph","created_at":"2026-05-18T00:09:21Z","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":"Borwein and Choi conjectured that a polynomial $P(x)$ with coefficients $\\pm1$ of degree $N-1$ is cyclotomic iff $$P(x)=\\pm \\Phi_{p_1}(\\pm x)\\Phi_{p_2}(\\pm x^{p_1})\\cdots \\Phi_{p_r}(\\pm x^{p_1p_2\\cdots p_{r-1}})$$ where $N=p_1p_2\\cdots p_{r}$ and the $p_i$ are primes, not necessarily distinct. Here $\\Phi_p(x):=(x^p-1)/(x-1)$ is the $p-$th cyclotomic polynomial. In \\cite{1}, they also proved the conjecture for $N$ odd or a power of 2. In this paper we introduce a so-called $E-$transformation, by which we prove the conjecture for a wider variety of cases and present the key as well as a new appr","authors_text":"Shaofang Hong, Wei Cao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-31T07:49:11Z","title":"Notes On a Borwein and Choi's conjecture of cyclotomic polynomials with coefficients $\\pm1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11693","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:d9b2cbd9807576debbfcfb6ae83fbb52e5be6bff892e26f87d907a1d178f72d0","target":"record","created_at":"2026-05-18T00:09:21Z","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":"60cca542999091d789be93675a28d8ca8fc31827e1651a8be8dc0d8d09462ba2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-31T07:49:11Z","title_canon_sha256":"9134077e7e486a18260cb4dbf5d789efa54c6af6e0d8c62aafa12f2c44013fb4"},"schema_version":"1.0","source":{"id":"1807.11693","kind":"arxiv","version":1}},"canonical_sha256":"ea76b1e9f64699fc743b6946b6b72d7cc53234476a37609aa4409b9670eddf6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea76b1e9f64699fc743b6946b6b72d7cc53234476a37609aa4409b9670eddf6a","first_computed_at":"2026-05-18T00:09:21.361892Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:21.361892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4gKT8+zQ0v+Kpafh6COiecttV/ZgrG1TohdBTj0UsfFYH+kbbWc1gSJNf0CSe1/Em1HGnh5bcFaNolIbaRAUBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:21.362600Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.11693","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9b2cbd9807576debbfcfb6ae83fbb52e5be6bff892e26f87d907a1d178f72d0","sha256:4987321b10ed3f0a4ceebdb5e4aba7895a906aee72ecab5ef9df2e39fd556659"],"state_sha256":"7e807c89062b5ed192079d208086d69545af0c3d4f7ed7da43b7ff098924f699"}