{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:M3Y2QUOKTDJJKHHZJYANRMKYEV","short_pith_number":"pith:M3Y2QUOK","schema_version":"1.0","canonical_sha256":"66f1a851ca98d2951cf94e00d8b158255f5c3956d5c276fc26a27432bae09401","source":{"kind":"arxiv","id":"2601.21466","version":2},"attestation_state":"computed","paper":{"title":"A note on irreducible slice algebraic sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Anna Gori, Fabio Vlacci, Giulia Sarfatti","submitted_at":"2026-01-29T09:42:12Z","abstract_excerpt":"In this short note we prove that if $I$ is a right radical and quasi prime ideal in the ring of quaternionic slice regular polynomials, then the symmetrization $\\mathbb S_{V_c(I)}$ is an irreducible algebraic set, where $V_c(I)$ is the set of common zeros with commuting components of polynomials in $I$. Combining this fact with the results proved in our previous paper [3], we obtain that for $I$ radical, $V_c(I)$ is irreducible if and only if $I$ is quasi prime."},"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":"2601.21466","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-01-29T09:42:12Z","cross_cats_sorted":[],"title_canon_sha256":"f9bab062f409e010691693d25a6f7bc1df7b7c29bd3b227782b7a250435d05c5","abstract_canon_sha256":"5ed3ed95db54c56b377bccd3803dff91b37808d5cbf01f846047f6c381aa15f8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:05:07.138677Z","signature_b64":"dTYFNs4RxdSOFJ94eolGh0Q2MYprw4Sf0xM82raH0PTsDOryhs4LuFRezVh5jWjyC6wb1sL8hmb3Wo3XXcpdDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66f1a851ca98d2951cf94e00d8b158255f5c3956d5c276fc26a27432bae09401","last_reissued_at":"2026-05-20T01:05:07.137818Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:05:07.137818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on irreducible slice algebraic sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Anna Gori, Fabio Vlacci, Giulia Sarfatti","submitted_at":"2026-01-29T09:42:12Z","abstract_excerpt":"In this short note we prove that if $I$ is a right radical and quasi prime ideal in the ring of quaternionic slice regular polynomials, then the symmetrization $\\mathbb S_{V_c(I)}$ is an irreducible algebraic set, where $V_c(I)$ is the set of common zeros with commuting components of polynomials in $I$. Combining this fact with the results proved in our previous paper [3], we obtain that for $I$ radical, $V_c(I)$ is irreducible if and only if $I$ is quasi prime."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.21466","kind":"arxiv","version":2},"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/2601.21466/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":"2601.21466","created_at":"2026-05-20T01:05:07.137940+00:00"},{"alias_kind":"arxiv_version","alias_value":"2601.21466v2","created_at":"2026-05-20T01:05:07.137940+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.21466","created_at":"2026-05-20T01:05:07.137940+00:00"},{"alias_kind":"pith_short_12","alias_value":"M3Y2QUOKTDJJ","created_at":"2026-05-20T01:05:07.137940+00:00"},{"alias_kind":"pith_short_16","alias_value":"M3Y2QUOKTDJJKHHZ","created_at":"2026-05-20T01:05:07.137940+00:00"},{"alias_kind":"pith_short_8","alias_value":"M3Y2QUOK","created_at":"2026-05-20T01:05:07.137940+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/M3Y2QUOKTDJJKHHZJYANRMKYEV","json":"https://pith.science/pith/M3Y2QUOKTDJJKHHZJYANRMKYEV.json","graph_json":"https://pith.science/api/pith-number/M3Y2QUOKTDJJKHHZJYANRMKYEV/graph.json","events_json":"https://pith.science/api/pith-number/M3Y2QUOKTDJJKHHZJYANRMKYEV/events.json","paper":"https://pith.science/paper/M3Y2QUOK"},"agent_actions":{"view_html":"https://pith.science/pith/M3Y2QUOKTDJJKHHZJYANRMKYEV","download_json":"https://pith.science/pith/M3Y2QUOKTDJJKHHZJYANRMKYEV.json","view_paper":"https://pith.science/paper/M3Y2QUOK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2601.21466&json=true","fetch_graph":"https://pith.science/api/pith-number/M3Y2QUOKTDJJKHHZJYANRMKYEV/graph.json","fetch_events":"https://pith.science/api/pith-number/M3Y2QUOKTDJJKHHZJYANRMKYEV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M3Y2QUOKTDJJKHHZJYANRMKYEV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M3Y2QUOKTDJJKHHZJYANRMKYEV/action/storage_attestation","attest_author":"https://pith.science/pith/M3Y2QUOKTDJJKHHZJYANRMKYEV/action/author_attestation","sign_citation":"https://pith.science/pith/M3Y2QUOKTDJJKHHZJYANRMKYEV/action/citation_signature","submit_replication":"https://pith.science/pith/M3Y2QUOKTDJJKHHZJYANRMKYEV/action/replication_record"}},"created_at":"2026-05-20T01:05:07.137940+00:00","updated_at":"2026-05-20T01:05:07.137940+00:00"}