{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VR6EFZT5X4H7GQEU4T2CR6EIF3","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":"a08f94b050fbf1dac3784b882b73c82a17ed7a51afa03d3f674a5881dc218f76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-09T03:25:13Z","title_canon_sha256":"874004d75d4317e31b12a5d5f292e1deeb07e5944ffe2dabed4b0ad706ff149b"},"schema_version":"1.0","source":{"id":"1907.03959","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.03959","created_at":"2026-05-17T23:41:06Z"},{"alias_kind":"arxiv_version","alias_value":"1907.03959v1","created_at":"2026-05-17T23:41:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.03959","created_at":"2026-05-17T23:41:06Z"},{"alias_kind":"pith_short_12","alias_value":"VR6EFZT5X4H7","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VR6EFZT5X4H7GQEU","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VR6EFZT5","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:0d139d7a6fdec74a6b6a4a49fdf2d0a347adeb09d318fcf8a58c57eb384d58bc","target":"graph","created_at":"2026-05-17T23:41:06Z","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 article we study the irreducibility of polynomials of the form\n  $x^n+\\epsilon_1 x^m+p^k\\epsilon_2$, $p$ being a prime number. We will show that they are irreducible for $m=1$. We have also provided the cyclotomic factors and reducibility criterion for trinomials of the form $x^n+\\epsilon_1x^m+\\epsilon_2$, where $\\epsilon_i\\in \\{\\, -1,+1\\,\\}$. This corrects few of the existing results of W. Ljuggren's on $x^n+\\epsilon_1x^m+\\epsilon_2$.","authors_text":"A.Satyanarayana Reddy, Biswajit Koley","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-09T03:25:13Z","title":"Irreducibility criterion for certain trinomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03959","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:f3a19eebd9d8ed74cba5ddc070ffd3bc141245624caac323149901d1941b2651","target":"record","created_at":"2026-05-17T23:41:06Z","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":"a08f94b050fbf1dac3784b882b73c82a17ed7a51afa03d3f674a5881dc218f76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-07-09T03:25:13Z","title_canon_sha256":"874004d75d4317e31b12a5d5f292e1deeb07e5944ffe2dabed4b0ad706ff149b"},"schema_version":"1.0","source":{"id":"1907.03959","kind":"arxiv","version":1}},"canonical_sha256":"ac7c42e67dbf0ff34094e4f428f8882ee84bc101a7aa384cdd78969e72b02cee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac7c42e67dbf0ff34094e4f428f8882ee84bc101a7aa384cdd78969e72b02cee","first_computed_at":"2026-05-17T23:41:06.222441Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:06.222441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W+Tpeo9b7f9JH28WD2+BoojYCk3Gz+NudvJQ5drjAUcVSr2ut0PYYUnB9nfVj5oeW79o2qXs0o8+BqyEZYkwAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:06.223180Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.03959","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3a19eebd9d8ed74cba5ddc070ffd3bc141245624caac323149901d1941b2651","sha256:0d139d7a6fdec74a6b6a4a49fdf2d0a347adeb09d318fcf8a58c57eb384d58bc"],"state_sha256":"d922752b186d0f5d62506cc911d98ba816178583e2208445968501203caeb331"}