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Then $ad\\, C_{q(X)}$ has such highly unusual properties that any $A\\in{\\mathfrak{ gl}}(m)$ such that $ad\\, A$ has like properties is shown to be similar to the companion matrix of an irreducible generalized Artin-Schreier polynomial.\n  We discuss close connections with the decomposition problem of the tensor product of indecomposable modules f"},"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":"1306.3967","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-06-17T19:45:07Z","cross_cats_sorted":[],"title_canon_sha256":"5c906beaabaaece834b4f61875d5edc80c9045683a7fbdd9f3c5ed7754d3d955","abstract_canon_sha256":"ff4ad0a54e480a9dc3e379929e63aa29bf97b4209b8de61942290195af554038"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:56.958938Z","signature_b64":"AvNsMaLK8QETwrwYj6jxnZPzzmW6KqvcQU3X1pn+HukgMXM+fGNWMyDyDyJebEBo1tIfHKf9ds9IP0ugGdnABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac547e136728d9c98c19f828ec1b73eb8eb551ba967e6386c66bee19966829d9","last_reissued_at":"2026-05-18T02:44:56.958461Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:56.958461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Artin-Schreier polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Fernando Szechtman, Natalio H. Guersenzvaig","submitted_at":"2013-06-17T19:45:07Z","abstract_excerpt":"Let $F$ be a field of prime characteristic $p$ containing $F_{p^n}$ as a subfield. We refer to $q(X)=X^{p^n}-X-a\\in F[X]$ as a generalized Artin-Schreier polynomial. Suppose that $q(X)$ is irreducible and let $C_{q(X)}$ be the companion matrix of $q(X)$. Then $ad\\, C_{q(X)}$ has such highly unusual properties that any $A\\in{\\mathfrak{ gl}}(m)$ such that $ad\\, A$ has like properties is shown to be similar to the companion matrix of an irreducible generalized Artin-Schreier polynomial.\n  We discuss close connections with the decomposition problem of the tensor product of indecomposable modules f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3967","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1306.3967","created_at":"2026-05-18T02:44:56.958541+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.3967v4","created_at":"2026-05-18T02:44:56.958541+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3967","created_at":"2026-05-18T02:44:56.958541+00:00"},{"alias_kind":"pith_short_12","alias_value":"VRKH4E3HFDM4","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"VRKH4E3HFDM4TDAZ","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"VRKH4E3H","created_at":"2026-05-18T12:28:04.890932+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/VRKH4E3HFDM4TDAZ7AUOYG3T5O","json":"https://pith.science/pith/VRKH4E3HFDM4TDAZ7AUOYG3T5O.json","graph_json":"https://pith.science/api/pith-number/VRKH4E3HFDM4TDAZ7AUOYG3T5O/graph.json","events_json":"https://pith.science/api/pith-number/VRKH4E3HFDM4TDAZ7AUOYG3T5O/events.json","paper":"https://pith.science/paper/VRKH4E3H"},"agent_actions":{"view_html":"https://pith.science/pith/VRKH4E3HFDM4TDAZ7AUOYG3T5O","download_json":"https://pith.science/pith/VRKH4E3HFDM4TDAZ7AUOYG3T5O.json","view_paper":"https://pith.science/paper/VRKH4E3H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.3967&json=true","fetch_graph":"https://pith.science/api/pith-number/VRKH4E3HFDM4TDAZ7AUOYG3T5O/graph.json","fetch_events":"https://pith.science/api/pith-number/VRKH4E3HFDM4TDAZ7AUOYG3T5O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VRKH4E3HFDM4TDAZ7AUOYG3T5O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VRKH4E3HFDM4TDAZ7AUOYG3T5O/action/storage_attestation","attest_author":"https://pith.science/pith/VRKH4E3HFDM4TDAZ7AUOYG3T5O/action/author_attestation","sign_citation":"https://pith.science/pith/VRKH4E3HFDM4TDAZ7AUOYG3T5O/action/citation_signature","submit_replication":"https://pith.science/pith/VRKH4E3HFDM4TDAZ7AUOYG3T5O/action/replication_record"}},"created_at":"2026-05-18T02:44:56.958541+00:00","updated_at":"2026-05-18T02:44:56.958541+00:00"}