{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:WGVVAHQLF53EFOCVYYHMUED7LE","short_pith_number":"pith:WGVVAHQL","schema_version":"1.0","canonical_sha256":"b1ab501e0b2f7642b855c60eca107f591e3c01cdec43211549391fa607619481","source":{"kind":"arxiv","id":"2606.09739","version":1},"attestation_state":"computed","paper":{"title":"Power Integral Bases in Polynomial Compositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aakash Choudhary, Prabhakar Yadav, Supriya Pisolkar","submitted_at":"2026-06-08T17:02:42Z","abstract_excerpt":"In this paper, we study the monogeneity of a special class of composed polynomials of the form $\n(f \\circ g)(x) = (x^m + c)^n + a(x^m + c)^{n-1} + d(x^m + c)^{n-2} + b,$ where \\( f(x) = x^n + a x^{n-1} + d x^{n-2} + b \\in \\mathbb{Z}[x] \\) satisfies \\( a^2 = 4d \\) and \\( g(x) = x^m + c \\in \\mathbb{Z}[x] \\). 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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.09739","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-08T17:02:42Z","cross_cats_sorted":[],"title_canon_sha256":"64b0aebf8135aa70463c12967948fa16edcfc2b540098fd2a9b74c540c1aed1b","abstract_canon_sha256":"4971771529c006c37c0e8ce5ff927f0d05a10786f597db33420180d38ed97b42"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:09:07.012732Z","signature_b64":"yeS+v6K9qlgTPtzbIP9dFCoV1Ziftq6z7spdDPsSUnzWTSS18vBOU9gjgrZKOn1cM2AHIGkpqY4Y/3N3HsnrCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1ab501e0b2f7642b855c60eca107f591e3c01cdec43211549391fa607619481","last_reissued_at":"2026-06-09T02:09:07.011878Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:09:07.011878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Power Integral Bases in Polynomial Compositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aakash Choudhary, Prabhakar Yadav, Supriya Pisolkar","submitted_at":"2026-06-08T17:02:42Z","abstract_excerpt":"In this paper, we study the monogeneity of a special class of composed polynomials of the form $\n(f \\circ g)(x) = (x^m + c)^n + a(x^m + c)^{n-1} + d(x^m + c)^{n-2} + b,$ where \\( f(x) = x^n + a x^{n-1} + d x^{n-2} + b \\in \\mathbb{Z}[x] \\) satisfies \\( a^2 = 4d \\) and \\( g(x) = x^m + c \\in \\mathbb{Z}[x] \\). 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09739","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.09739/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.09739","created_at":"2026-06-09T02:09:07.011999+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.09739v1","created_at":"2026-06-09T02:09:07.011999+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09739","created_at":"2026-06-09T02:09:07.011999+00:00"},{"alias_kind":"pith_short_12","alias_value":"WGVVAHQLF53E","created_at":"2026-06-09T02:09:07.011999+00:00"},{"alias_kind":"pith_short_16","alias_value":"WGVVAHQLF53EFOCV","created_at":"2026-06-09T02:09:07.011999+00:00"},{"alias_kind":"pith_short_8","alias_value":"WGVVAHQL","created_at":"2026-06-09T02:09:07.011999+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WGVVAHQLF53EFOCVYYHMUED7LE","json":"https://pith.science/pith/WGVVAHQLF53EFOCVYYHMUED7LE.json","graph_json":"https://pith.science/api/pith-number/WGVVAHQLF53EFOCVYYHMUED7LE/graph.json","events_json":"https://pith.science/api/pith-number/WGVVAHQLF53EFOCVYYHMUED7LE/events.json","paper":"https://pith.science/paper/WGVVAHQL"},"agent_actions":{"view_html":"https://pith.science/pith/WGVVAHQLF53EFOCVYYHMUED7LE","download_json":"https://pith.science/pith/WGVVAHQLF53EFOCVYYHMUED7LE.json","view_paper":"https://pith.science/paper/WGVVAHQL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.09739&json=true","fetch_graph":"https://pith.science/api/pith-number/WGVVAHQLF53EFOCVYYHMUED7LE/graph.json","fetch_events":"https://pith.science/api/pith-number/WGVVAHQLF53EFOCVYYHMUED7LE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WGVVAHQLF53EFOCVYYHMUED7LE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WGVVAHQLF53EFOCVYYHMUED7LE/action/storage_attestation","attest_author":"https://pith.science/pith/WGVVAHQLF53EFOCVYYHMUED7LE/action/author_attestation","sign_citation":"https://pith.science/pith/WGVVAHQLF53EFOCVYYHMUED7LE/action/citation_signature","submit_replication":"https://pith.science/pith/WGVVAHQLF53EFOCVYYHMUED7LE/action/replication_record"}},"created_at":"2026-06-09T02:09:07.011999+00:00","updated_at":"2026-06-09T02:09:07.011999+00:00"}