{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:XV463H6JPF3POYEAHUFZD4GUNO","short_pith_number":"pith:XV463H6J","schema_version":"1.0","canonical_sha256":"bd79ed9fc97976f760803d0b91f0d46ba5b502ca538e12015001dafb5802f274","source":{"kind":"arxiv","id":"1905.04163","version":1},"attestation_state":"computed","paper":{"title":"The Nullstellensatz for supersymmetric polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.RA","authors_text":"Ian M. Musson","submitted_at":"2019-05-10T13:29:43Z","abstract_excerpt":"In this paper we prove a Nullstellensatz for supersymmetric polynomials. This gives a bijection between radical ideals and superalgebraic sets. These are algebraic sets which are invariant under the Weyl groupoid of Sergeev and Veselov, \\cite{SV2}. Note that the algebra of supersymmetric polynomials is not Noetherian, so the usual Nullstellensatz does not apply. However it deos satisfy the ascending chain condition on radical ideals and this allows for the decomposition of superalgebraic sets into irreducible components. Analogous results hold for the a ring of Laurent supersymmetric polynomia"},"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":"1905.04163","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-05-10T13:29:43Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"5c3d155e4f0e2ddfd10c84e21202f428bfd57d6fd4c270e7ebf4434f12333abe","abstract_canon_sha256":"2a1c5700d420c885aadc91db6c01eaa2b6db6284d5294448fc8c124388e8b596"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:34.326224Z","signature_b64":"gUFOMGNBzut+rLwRqFaeiN2UsPmE9VITfWILPX3fe9IZ61XbFtdRdMFdQDfSEyUEXqDs7SHatO+RdxuMlar5Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd79ed9fc97976f760803d0b91f0d46ba5b502ca538e12015001dafb5802f274","last_reissued_at":"2026-05-17T23:46:34.325547Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:34.325547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Nullstellensatz for supersymmetric polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.RA","authors_text":"Ian M. Musson","submitted_at":"2019-05-10T13:29:43Z","abstract_excerpt":"In this paper we prove a Nullstellensatz for supersymmetric polynomials. This gives a bijection between radical ideals and superalgebraic sets. These are algebraic sets which are invariant under the Weyl groupoid of Sergeev and Veselov, \\cite{SV2}. Note that the algebra of supersymmetric polynomials is not Noetherian, so the usual Nullstellensatz does not apply. However it deos satisfy the ascending chain condition on radical ideals and this allows for the decomposition of superalgebraic sets into irreducible components. Analogous results hold for the a ring of Laurent supersymmetric polynomia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04163","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":""},"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":"1905.04163","created_at":"2026-05-17T23:46:34.325661+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.04163v1","created_at":"2026-05-17T23:46:34.325661+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04163","created_at":"2026-05-17T23:46:34.325661+00:00"},{"alias_kind":"pith_short_12","alias_value":"XV463H6JPF3P","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_16","alias_value":"XV463H6JPF3POYEA","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_8","alias_value":"XV463H6J","created_at":"2026-05-18T12:33:33.725879+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/XV463H6JPF3POYEAHUFZD4GUNO","json":"https://pith.science/pith/XV463H6JPF3POYEAHUFZD4GUNO.json","graph_json":"https://pith.science/api/pith-number/XV463H6JPF3POYEAHUFZD4GUNO/graph.json","events_json":"https://pith.science/api/pith-number/XV463H6JPF3POYEAHUFZD4GUNO/events.json","paper":"https://pith.science/paper/XV463H6J"},"agent_actions":{"view_html":"https://pith.science/pith/XV463H6JPF3POYEAHUFZD4GUNO","download_json":"https://pith.science/pith/XV463H6JPF3POYEAHUFZD4GUNO.json","view_paper":"https://pith.science/paper/XV463H6J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.04163&json=true","fetch_graph":"https://pith.science/api/pith-number/XV463H6JPF3POYEAHUFZD4GUNO/graph.json","fetch_events":"https://pith.science/api/pith-number/XV463H6JPF3POYEAHUFZD4GUNO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XV463H6JPF3POYEAHUFZD4GUNO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XV463H6JPF3POYEAHUFZD4GUNO/action/storage_attestation","attest_author":"https://pith.science/pith/XV463H6JPF3POYEAHUFZD4GUNO/action/author_attestation","sign_citation":"https://pith.science/pith/XV463H6JPF3POYEAHUFZD4GUNO/action/citation_signature","submit_replication":"https://pith.science/pith/XV463H6JPF3POYEAHUFZD4GUNO/action/replication_record"}},"created_at":"2026-05-17T23:46:34.325661+00:00","updated_at":"2026-05-17T23:46:34.325661+00:00"}