{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OUFNLJ34RQ4XBLUKVYYOPBUS7M","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":"e14f031970b3dc3958eeea05faa470f645c4140fc824a9dc3a51f3b4c073aa2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-07T11:42:50Z","title_canon_sha256":"3363d66a0b702f5fcb3a829ad7196abc944df4b7ea38c9119d5a08b11727529d"},"schema_version":"1.0","source":{"id":"1602.02361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02361","created_at":"2026-05-18T00:32:31Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02361v1","created_at":"2026-05-18T00:32:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02361","created_at":"2026-05-18T00:32:31Z"},{"alias_kind":"pith_short_12","alias_value":"OUFNLJ34RQ4X","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OUFNLJ34RQ4XBLUK","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OUFNLJ34","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:0d31a10bd8f97843d4508def5960bffc313e3c8cb40a8418adce9a292e88d3a2","target":"graph","created_at":"2026-05-18T00:32:31Z","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":"We give a new proof of the Brawley-Carlitz theorem on irreducibility of the composed products of irreducible polynomials. Our proof shows that associativity of the binary operation for the composed product is not necessary. We then investigate binary operations defined by polynomial functions, and give a sufficient condition in terms of degrees for the requirement in the Brawley-Carlitz theorem.","authors_text":"Akihiro Munemasa, Hiroko Nakamura","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-07T11:42:50Z","title":"A note on the Brawley-Carlitz theorem on irreducibility of composed products of polynomials over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02361","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:c9fb4ec3e7cbc7667c7dd6d440f39143fa40548218df8d88d558dcc9d75491f7","target":"record","created_at":"2026-05-18T00:32:31Z","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":"e14f031970b3dc3958eeea05faa470f645c4140fc824a9dc3a51f3b4c073aa2a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-02-07T11:42:50Z","title_canon_sha256":"3363d66a0b702f5fcb3a829ad7196abc944df4b7ea38c9119d5a08b11727529d"},"schema_version":"1.0","source":{"id":"1602.02361","kind":"arxiv","version":1}},"canonical_sha256":"750ad5a77c8c3970ae8aae30e78692fb09bbdfaa817c682e6e0d0950fca36ca0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"750ad5a77c8c3970ae8aae30e78692fb09bbdfaa817c682e6e0d0950fca36ca0","first_computed_at":"2026-05-18T00:32:31.489448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:31.489448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ArPo1pgQ0vVfplNkylbBSbQMtGrThSPeD4h2BnnMwlooKRaBco/XEky02A0mTO0np62cuSa5VtU8teCytnm7DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:31.490086Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.02361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9fb4ec3e7cbc7667c7dd6d440f39143fa40548218df8d88d558dcc9d75491f7","sha256:0d31a10bd8f97843d4508def5960bffc313e3c8cb40a8418adce9a292e88d3a2"],"state_sha256":"cada2b728de31e705f852e289131cfccdfdea62de376f0baec82ae0338299300"}