{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:DBMY6U3HAFUVP44VERSIWUVPOZ","short_pith_number":"pith:DBMY6U3H","schema_version":"1.0","canonical_sha256":"18598f5367016957f39524648b52af764125fe44c05ba1b775ccce3a12b377e3","source":{"kind":"arxiv","id":"1706.01279","version":2},"attestation_state":"computed","paper":{"title":"On the Dixmier-Moeglin equivalence for Poisson-Hopf algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Omar Le\\'on S\\'anchez, St\\'ephane Launois","submitted_at":"2017-06-05T11:39:30Z","abstract_excerpt":"We prove that the Poisson version of the Dixmier-Moeglin equivalence holds for cocommutative affine Poisson-Hopf algebras. This is a first step towards understanding the symplectic foliation and the representation theory of (cocommutative) affine Poisson-Hopf algebras. Our proof makes substantial use of the model theory of fields equipped with finitely many possibly noncommuting derivations. As an application, we show that the symmetric algebra of a finite dimensional Lie algebra, equipped with its natural Poisson structure, satisfies the Poisson Dixmier-Moeglin equivalence."},"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":"1706.01279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-06-05T11:39:30Z","cross_cats_sorted":[],"title_canon_sha256":"89f79c6de4935fc9a7b2b32c19234bd086fdea9e5cb8aecf430982147f0f2e2c","abstract_canon_sha256":"725c4f67cf2c8adbd41a781be3dc3306aced502bca7a21a13994eec2e8998f16"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:59.764908Z","signature_b64":"d3s15jXTHpegrkKpq/TkqirYbekzMEk/PizuZhLvJ/+kCJ7TeHkifFEtyCvI1pe9ugLJxHIGzRQq2SVdWuY5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18598f5367016957f39524648b52af764125fe44c05ba1b775ccce3a12b377e3","last_reissued_at":"2026-05-18T00:30:59.764330Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:59.764330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Dixmier-Moeglin equivalence for Poisson-Hopf algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Omar Le\\'on S\\'anchez, St\\'ephane Launois","submitted_at":"2017-06-05T11:39:30Z","abstract_excerpt":"We prove that the Poisson version of the Dixmier-Moeglin equivalence holds for cocommutative affine Poisson-Hopf algebras. This is a first step towards understanding the symplectic foliation and the representation theory of (cocommutative) affine Poisson-Hopf algebras. Our proof makes substantial use of the model theory of fields equipped with finitely many possibly noncommuting derivations. As an application, we show that the symmetric algebra of a finite dimensional Lie algebra, equipped with its natural Poisson structure, satisfies the Poisson Dixmier-Moeglin equivalence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01279","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":""},"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":"1706.01279","created_at":"2026-05-18T00:30:59.764428+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.01279v2","created_at":"2026-05-18T00:30:59.764428+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.01279","created_at":"2026-05-18T00:30:59.764428+00:00"},{"alias_kind":"pith_short_12","alias_value":"DBMY6U3HAFUV","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"DBMY6U3HAFUVP44V","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"DBMY6U3H","created_at":"2026-05-18T12:31:10.602751+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/DBMY6U3HAFUVP44VERSIWUVPOZ","json":"https://pith.science/pith/DBMY6U3HAFUVP44VERSIWUVPOZ.json","graph_json":"https://pith.science/api/pith-number/DBMY6U3HAFUVP44VERSIWUVPOZ/graph.json","events_json":"https://pith.science/api/pith-number/DBMY6U3HAFUVP44VERSIWUVPOZ/events.json","paper":"https://pith.science/paper/DBMY6U3H"},"agent_actions":{"view_html":"https://pith.science/pith/DBMY6U3HAFUVP44VERSIWUVPOZ","download_json":"https://pith.science/pith/DBMY6U3HAFUVP44VERSIWUVPOZ.json","view_paper":"https://pith.science/paper/DBMY6U3H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.01279&json=true","fetch_graph":"https://pith.science/api/pith-number/DBMY6U3HAFUVP44VERSIWUVPOZ/graph.json","fetch_events":"https://pith.science/api/pith-number/DBMY6U3HAFUVP44VERSIWUVPOZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DBMY6U3HAFUVP44VERSIWUVPOZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DBMY6U3HAFUVP44VERSIWUVPOZ/action/storage_attestation","attest_author":"https://pith.science/pith/DBMY6U3HAFUVP44VERSIWUVPOZ/action/author_attestation","sign_citation":"https://pith.science/pith/DBMY6U3HAFUVP44VERSIWUVPOZ/action/citation_signature","submit_replication":"https://pith.science/pith/DBMY6U3HAFUVP44VERSIWUVPOZ/action/replication_record"}},"created_at":"2026-05-18T00:30:59.764428+00:00","updated_at":"2026-05-18T00:30:59.764428+00:00"}