{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:M3Y2QUOKTDJJKHHZJYANRMKYEV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5ed3ed95db54c56b377bccd3803dff91b37808d5cbf01f846047f6c381aa15f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-01-29T09:42:12Z","title_canon_sha256":"f9bab062f409e010691693d25a6f7bc1df7b7c29bd3b227782b7a250435d05c5"},"schema_version":"1.0","source":{"id":"2601.21466","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.21466","created_at":"2026-05-20T01:05:07Z"},{"alias_kind":"arxiv_version","alias_value":"2601.21466v2","created_at":"2026-05-20T01:05:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.21466","created_at":"2026-05-20T01:05:07Z"},{"alias_kind":"pith_short_12","alias_value":"M3Y2QUOKTDJJ","created_at":"2026-05-20T01:05:07Z"},{"alias_kind":"pith_short_16","alias_value":"M3Y2QUOKTDJJKHHZ","created_at":"2026-05-20T01:05:07Z"},{"alias_kind":"pith_short_8","alias_value":"M3Y2QUOK","created_at":"2026-05-20T01:05:07Z"}],"graph_snapshots":[{"event_id":"sha256:42402ef2c2265948846acecccc53623293249a66b532fb01358c6505ebf9de59","target":"graph","created_at":"2026-05-20T01:05:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2601.21466/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"Anna Gori, Fabio Vlacci, Giulia Sarfatti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-01-29T09:42:12Z","title":"A note on irreducible slice algebraic sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.21466","kind":"arxiv","version":2},"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:bd18724a10bb7fc7bd76ea37c133beb2553cb97d43546a7e4fb51e8515d164fd","target":"record","created_at":"2026-05-20T01:05:07Z","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":"5ed3ed95db54c56b377bccd3803dff91b37808d5cbf01f846047f6c381aa15f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-01-29T09:42:12Z","title_canon_sha256":"f9bab062f409e010691693d25a6f7bc1df7b7c29bd3b227782b7a250435d05c5"},"schema_version":"1.0","source":{"id":"2601.21466","kind":"arxiv","version":2}},"canonical_sha256":"66f1a851ca98d2951cf94e00d8b158255f5c3956d5c276fc26a27432bae09401","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66f1a851ca98d2951cf94e00d8b158255f5c3956d5c276fc26a27432bae09401","first_computed_at":"2026-05-20T01:05:07.137818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T01:05:07.137818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dTYFNs4RxdSOFJ94eolGh0Q2MYprw4Sf0xM82raH0PTsDOryhs4LuFRezVh5jWjyC6wb1sL8hmb3Wo3XXcpdDw==","signature_status":"signed_v1","signed_at":"2026-05-20T01:05:07.138677Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.21466","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd18724a10bb7fc7bd76ea37c133beb2553cb97d43546a7e4fb51e8515d164fd","sha256:42402ef2c2265948846acecccc53623293249a66b532fb01358c6505ebf9de59"],"state_sha256":"eb1d4f40f13a103b0f9a7bb95c70cee20aaf22243906f3d7e871ac36ac33ffa0"}