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A square sign pattern matrix $S$ is said to allow algebraic positivity if there is an algebraically positive matrix $M$ whose sign pattern class is $S$. On the other hand, $S$ is said to require algebraic positivity if any matrix $M$, having sign pattern class $S$, is algebraically positive. Motivated by open problems raised in the work of Kirkland, Qiao and Zhan (2016) on AP matrices, we list down all nonequivalent irreducible $3\\t"},"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":"1806.09641","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-25T18:00:18Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"970a4667decc7ef4b8087dbcd7fdc83c55f36052da7e5c15d960a06d02d68112","abstract_canon_sha256":"d99e5e7af331cd58667730399b39c5a466b3a54a84eb1b6fa3c6349a04b70343"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:15.090983Z","signature_b64":"fvoqGC6Wtyvudh1fuOQymxjzg+xz8mqsdfRvY2211vFjIlIzlcjygbF0ckdi7jtG/lIgg1IQ7jg7BXIiwyRVAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0603930bfaec72847eef0290be966a4948f14a9eec1652e3e2b0af1c98a0be8","last_reissued_at":"2026-05-17T23:56:15.090310Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:15.090310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Sign Pattern Matrices that Allow or Require Algebraic Positivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CO","authors_text":"Diane Christine Pelejo, Jean Leonardo Abagat","submitted_at":"2018-06-25T18:00:18Z","abstract_excerpt":"A square matrix $M$ with real entries is said to be algebraically positive (AP) if there exists a real polynomial $p$ such that all entries of the matrix $p(M)>0$. A square sign pattern matrix $S$ is said to allow algebraic positivity if there is an algebraically positive matrix $M$ whose sign pattern class is $S$. On the other hand, $S$ is said to require algebraic positivity if any matrix $M$, having sign pattern class $S$, is algebraically positive. 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