{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:BW6B7HAPKW3DNV575AFJK3GDLW","short_pith_number":"pith:BW6B7HAP","schema_version":"1.0","canonical_sha256":"0dbc1f9c0f55b636d7bfe80a956cc35db6e10d68368ae79c052d0e4d7e81a6fb","source":{"kind":"arxiv","id":"2605.03421","version":2},"attestation_state":"computed","paper":{"title":"A connection between minimal nilpotent orbits of types A and D via Hamiltonian reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The affine closure of the cotangent bundle to the minimal nilpotent orbit in type A equals a C* Hamiltonian reduction of the minimal nilpotent orbit closure in type D.","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Baohua Fu, Jie Liu","submitted_at":"2026-05-05T06:52:27Z","abstract_excerpt":"We establish a novel connection between the minimal nilpotent orbit $\\mathbb{O}_n$ in $\\mathfrak{sl}_n$ and the minimal nilpotent orbit closure $\\overline{\\mathbf{O}}_n$ in $\\mathfrak{so}_{2n+2}$, which differs from the shared-orbit paradigm of Brylinski and Kostant, where no direct type-A--type-D relation appears. More precisely, we show that the affine closure of the cotangent bundle $\\overline{T^*\\mathbb{O}_n}^{\\mathrm{aff}}$ is isomorphic to a $\\mathbb{C}^*$-Hamiltonian reduction of $\\overline{\\mathbf{O}}_n$. This provides a quasi-classical analogue of a quantum result of Levasseur and Sta"},"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":"2605.03421","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-05-05T06:52:27Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"11b2da907c20e897d5989cb7c0d68b7bf8e74a60976d30a20c2bdc26df54bd40","abstract_canon_sha256":"a97e69a05b9f59fa86ec4ba8871ee5686650750f814a2b3e9f9aa40cb895a5ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:06:09.727495Z","signature_b64":"IdqAoc+Eo3dZjorpzpbRQI2bf5d+g7y0LTZSCTnWWIyk9jSXFaiEtLwwgp9rL9BShlJhYc9eRjj2j8WEv5LgBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0dbc1f9c0f55b636d7bfe80a956cc35db6e10d68368ae79c052d0e4d7e81a6fb","last_reissued_at":"2026-05-20T01:06:09.726922Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:06:09.726922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A connection between minimal nilpotent orbits of types A and D via Hamiltonian reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The affine closure of the cotangent bundle to the minimal nilpotent orbit in type A equals a C* Hamiltonian reduction of the minimal nilpotent orbit closure in type D.","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Baohua Fu, Jie Liu","submitted_at":"2026-05-05T06:52:27Z","abstract_excerpt":"We establish a novel connection between the minimal nilpotent orbit $\\mathbb{O}_n$ in $\\mathfrak{sl}_n$ and the minimal nilpotent orbit closure $\\overline{\\mathbf{O}}_n$ in $\\mathfrak{so}_{2n+2}$, which differs from the shared-orbit paradigm of Brylinski and Kostant, where no direct type-A--type-D relation appears. More precisely, we show that the affine closure of the cotangent bundle $\\overline{T^*\\mathbb{O}_n}^{\\mathrm{aff}}$ is isomorphic to a $\\mathbb{C}^*$-Hamiltonian reduction of $\\overline{\\mathbf{O}}_n$. This provides a quasi-classical analogue of a quantum result of Levasseur and Sta"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the affine closure of the cotangent bundle T*O_n^aff is isomorphic to a C*-Hamiltonian reduction of the minimal nilpotent orbit closure O_n in so_{2n+2}","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the chosen C* action on the orbit closure admits a well-defined moment map whose Hamiltonian reduction yields an isomorphism to the affine cotangent bundle closure, and that the subsequent geometric analysis correctly detects the non-existence of a symplectic resolution.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The affine closure of the cotangent bundle of the minimal nilpotent orbit O_n in sl_n is isomorphic to a C*-Hamiltonian reduction of the minimal nilpotent orbit closure in so_{2n+2}.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The affine closure of the cotangent bundle to the minimal nilpotent orbit in type A equals a C* Hamiltonian reduction of the minimal nilpotent orbit closure in type D.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3c5242bf5116248240601c60c8a3821e7f811b49020ffd690b5b191c4d67b942"},"source":{"id":"2605.03421","kind":"arxiv","version":2},"verdict":{"id":"28268538-dfab-4336-a472-9850ca0d3300","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T12:42:46.988673Z","strongest_claim":"the affine closure of the cotangent bundle T*O_n^aff is isomorphic to a C*-Hamiltonian reduction of the minimal nilpotent orbit closure O_n in so_{2n+2}","one_line_summary":"The affine closure of the cotangent bundle of the minimal nilpotent orbit O_n in sl_n is isomorphic to a C*-Hamiltonian reduction of the minimal nilpotent orbit closure in so_{2n+2}.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the chosen C* action on the orbit closure admits a well-defined moment map whose Hamiltonian reduction yields an isomorphism to the affine cotangent bundle closure, and that the subsequent geometric analysis correctly detects the non-existence of a symplectic resolution.","pith_extraction_headline":"The affine closure of the cotangent bundle to the minimal nilpotent orbit in type A equals a C* Hamiltonian reduction of the minimal nilpotent orbit closure in type D."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.03421/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-20T01:01:22.125205Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T15:25:37.985795Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"55c475fbb5115824a8640b02bbc2d6b58b56dd65356ad89ace9b7a67f76e7a7f"},"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":"2605.03421","created_at":"2026-05-20T01:06:09.727006+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.03421v2","created_at":"2026-05-20T01:06:09.727006+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.03421","created_at":"2026-05-20T01:06:09.727006+00:00"},{"alias_kind":"pith_short_12","alias_value":"BW6B7HAPKW3D","created_at":"2026-05-20T01:06:09.727006+00:00"},{"alias_kind":"pith_short_16","alias_value":"BW6B7HAPKW3DNV57","created_at":"2026-05-20T01:06:09.727006+00:00"},{"alias_kind":"pith_short_8","alias_value":"BW6B7HAP","created_at":"2026-05-20T01:06:09.727006+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/BW6B7HAPKW3DNV575AFJK3GDLW","json":"https://pith.science/pith/BW6B7HAPKW3DNV575AFJK3GDLW.json","graph_json":"https://pith.science/api/pith-number/BW6B7HAPKW3DNV575AFJK3GDLW/graph.json","events_json":"https://pith.science/api/pith-number/BW6B7HAPKW3DNV575AFJK3GDLW/events.json","paper":"https://pith.science/paper/BW6B7HAP"},"agent_actions":{"view_html":"https://pith.science/pith/BW6B7HAPKW3DNV575AFJK3GDLW","download_json":"https://pith.science/pith/BW6B7HAPKW3DNV575AFJK3GDLW.json","view_paper":"https://pith.science/paper/BW6B7HAP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.03421&json=true","fetch_graph":"https://pith.science/api/pith-number/BW6B7HAPKW3DNV575AFJK3GDLW/graph.json","fetch_events":"https://pith.science/api/pith-number/BW6B7HAPKW3DNV575AFJK3GDLW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BW6B7HAPKW3DNV575AFJK3GDLW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BW6B7HAPKW3DNV575AFJK3GDLW/action/storage_attestation","attest_author":"https://pith.science/pith/BW6B7HAPKW3DNV575AFJK3GDLW/action/author_attestation","sign_citation":"https://pith.science/pith/BW6B7HAPKW3DNV575AFJK3GDLW/action/citation_signature","submit_replication":"https://pith.science/pith/BW6B7HAPKW3DNV575AFJK3GDLW/action/replication_record"}},"created_at":"2026-05-20T01:06:09.727006+00:00","updated_at":"2026-05-20T01:06:09.727006+00:00"}