{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VR6NG7MIXNZJXNDH7R3FSYGATG","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":"8c84165bf68fec6d2b87167bb8cf17098f043d743a23e3f299e762d42c8189ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-06-14T21:42:32Z","title_canon_sha256":"e34fce9cca1fcb97af6f5f2816bae6b3c5112521fd199326da1ca4fa9d55a1f8"},"schema_version":"1.0","source":{"id":"1206.4355","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.4355","created_at":"2026-05-18T03:53:06Z"},{"alias_kind":"arxiv_version","alias_value":"1206.4355v1","created_at":"2026-05-18T03:53:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4355","created_at":"2026-05-18T03:53:06Z"},{"alias_kind":"pith_short_12","alias_value":"VR6NG7MIXNZJ","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VR6NG7MIXNZJXNDH","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VR6NG7MI","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:b93fb4bf7a92cddc089eecfa2a58f12c16cfc4fb96ef597c5b6581d706640cc8","target":"graph","created_at":"2026-05-18T03:53:06Z","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":"In this paper, we examine a natural question concerning the divisors of the polynomial x^n-1: \"How often does x^n-1 have a divisor of every degree between 1 and n?\" In a previous paper, we considered the situation when x^n-1 is factored in Z[x]. In this paper, we replace Z[x] with F_p[x], where p is an arbitrary-but-fixed prime. We also consider those n where this condition holds for all p.","authors_text":"Lola Thompson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-06-14T21:42:32Z","title":"Variations on a question concerning the degrees of divisors of x^n-1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4355","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":"sha256:3ce614901910947683ebe288fe47bb48540ffca4942e35500d99af4021d99268","target":"record","created_at":"2026-05-18T03:53:06Z","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":"8c84165bf68fec6d2b87167bb8cf17098f043d743a23e3f299e762d42c8189ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-06-14T21:42:32Z","title_canon_sha256":"e34fce9cca1fcb97af6f5f2816bae6b3c5112521fd199326da1ca4fa9d55a1f8"},"schema_version":"1.0","source":{"id":"1206.4355","kind":"arxiv","version":1}},"canonical_sha256":"ac7cd37d88bb729bb467fc765960c0999696bfb41b9e8e0e9b3b828b5fc721ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac7cd37d88bb729bb467fc765960c0999696bfb41b9e8e0e9b3b828b5fc721ae","first_computed_at":"2026-05-18T03:53:06.119309Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:06.119309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ikvPvsFSfSyZBb9uKwaltIOK0ZeHCwTrdMMkkaay9kwURk4VNfyIkxVLyJ5M6+FcRnm4RlCzAJgrJDXzf4ZiAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:06.120076Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.4355","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ce614901910947683ebe288fe47bb48540ffca4942e35500d99af4021d99268","sha256:b93fb4bf7a92cddc089eecfa2a58f12c16cfc4fb96ef597c5b6581d706640cc8"],"state_sha256":"5b1fe7097c40c4fc426f5886b501bf8676a475a08e3256fb6be6b7424bbe8d8b"}