{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2CMRCVFDD7AYIOLBSLM3PFP6N4","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":"7fe50f5024f42c6ffa2e04e938f483a1a012352ce1b5b491e7df4e43324514a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-10T18:54:39Z","title_canon_sha256":"6bcd38cf9e8321dc6b6af456eb3888e3d691c1d5d9d02400f7ebe3550b5fe3b5"},"schema_version":"1.0","source":{"id":"1511.03226","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03226","created_at":"2026-05-18T01:27:07Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03226v2","created_at":"2026-05-18T01:27:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03226","created_at":"2026-05-18T01:27:07Z"},{"alias_kind":"pith_short_12","alias_value":"2CMRCVFDD7AY","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2CMRCVFDD7AYIOLB","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2CMRCVFD","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:926b60abaad9625d05195c78d391216fa1844d91a3e5612601d553e9ff37c0f6","target":"graph","created_at":"2026-05-18T01:27:07Z","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 $a(r,n)$ be $r$th coefficient of $n$th cyclotomic polynomial. Suzuki proved that $\\{a(r,n)|r\\geq 1,n\\geq 1\\}=\\mathbb{Z}$. If $m$ and $n$ are two natural numbers we prove an analogue of Suzuki's theorem for divisors of $x^n-1$ with exactly $m$ irreducible factors. We prove that for every finite sequence of integers $n_1,\\ldots,n_r$ there exists a divisor $f(x)=\\sum_{i=0}^{deg(f)}c_ix^i$ of $x^n-1$ for some $n\\in \\mathbb{N}$ such that $c_i=n_i$ for $1\\leq i \\leq r$. Let $H(r,n)$ denote the maximum absolute value of $r$th coefficient of divisors of $x^n-1$. In the last section of the paper we","authors_text":"Sai Teja Somu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-10T18:54:39Z","title":"On the coefficients of divisors of $x^n-1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03226","kind":"arxiv","version":2},"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":"sha256:113e632f466e7ffa5e69076a6d6e26411729195948376b54d1b359b47e9663c4","target":"record","created_at":"2026-05-18T01:27:07Z","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":"7fe50f5024f42c6ffa2e04e938f483a1a012352ce1b5b491e7df4e43324514a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-10T18:54:39Z","title_canon_sha256":"6bcd38cf9e8321dc6b6af456eb3888e3d691c1d5d9d02400f7ebe3550b5fe3b5"},"schema_version":"1.0","source":{"id":"1511.03226","kind":"arxiv","version":2}},"canonical_sha256":"d0991154a31fc184396192d9b795fe6f2c6d1234a06d54322e0d1ced8afc2af7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0991154a31fc184396192d9b795fe6f2c6d1234a06d54322e0d1ced8afc2af7","first_computed_at":"2026-05-18T01:27:07.162014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:07.162014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oNVdtooQ8JCiqEGSdCnyvkfDKFIXQVXywj803jxfOxTHUCFYY1L01cI5FXzzNWhV1SUINA8uhXBKBYWuFGjwDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:07.162955Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.03226","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:113e632f466e7ffa5e69076a6d6e26411729195948376b54d1b359b47e9663c4","sha256:926b60abaad9625d05195c78d391216fa1844d91a3e5612601d553e9ff37c0f6"],"state_sha256":"391db7171b3957283ba4f66d4880b5d8d78a32136a7dd0b851a54a7dbd97e90f"}