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Assuming that \\( (f \\circ g)(x) \\) is irreducible over \\( \\mathbb{Q} \\), we obtain necessary and sufficient conditions on the parameters \\( a, b, c, d, m, n \\) for the polynomial to be monogenic. These conditions help to identify when the set \\( \\{1, \\theta, \\dots, \\theta^{mn-1}\\} \\) forms a","authors_text":"Aakash Choudhary, Prabhakar Yadav, Supriya Pisolkar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-08T17:02:42Z","title":"Power Integral Bases in Polynomial Compositions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09739","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:e164381e165f0806655db0dffabb9e3e57ec70bf9debb85354042bbb56ba5d34","target":"record","created_at":"2026-06-09T02:09:07Z","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":"4971771529c006c37c0e8ce5ff927f0d05a10786f597db33420180d38ed97b42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-08T17:02:42Z","title_canon_sha256":"64b0aebf8135aa70463c12967948fa16edcfc2b540098fd2a9b74c540c1aed1b"},"schema_version":"1.0","source":{"id":"2606.09739","kind":"arxiv","version":1}},"canonical_sha256":"b1ab501e0b2f7642b855c60eca107f591e3c01cdec43211549391fa607619481","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1ab501e0b2f7642b855c60eca107f591e3c01cdec43211549391fa607619481","first_computed_at":"2026-06-09T02:09:07.011878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:09:07.011878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yeS+v6K9qlgTPtzbIP9dFCoV1Ziftq6z7spdDPsSUnzWTSS18vBOU9gjgrZKOn1cM2AHIGkpqY4Y/3N3HsnrCg==","signature_status":"signed_v1","signed_at":"2026-06-09T02:09:07.012732Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.09739","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e164381e165f0806655db0dffabb9e3e57ec70bf9debb85354042bbb56ba5d34","sha256:fad4908a6e2f0ecf15f9339a7225898505e3a7ec5c536c62b48841f57fb27f36"],"state_sha256":"c9f760e80d2a150b8705073909b11acaab7dbb22410d7add5dfb69bb6b0fdb5c"}