{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:VGH7LJOLFTVTAKTZMDUBCDBI46","short_pith_number":"pith:VGH7LJOL","schema_version":"1.0","canonical_sha256":"a98ff5a5cb2ceb302a7960e8110c28e7ae5c420adf58417d6e8ea3fe0437d501","source":{"kind":"arxiv","id":"1205.1834","version":1},"attestation_state":"computed","paper":{"title":"The degenerate C. Neumann system I: symmetry reduction and convexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG","nlin.SI"],"primary_cat":"math.DS","authors_text":"Heinz Han{\\ss}mann, Holger R. Dullin","submitted_at":"2012-05-08T21:40:24Z","abstract_excerpt":"The C. Neumann system describes a particle on the sphere S^n under the influence of a potential that is a quadratic form. We study the case that the quadratic form has l+1 distinct eigenvalues with multiplicity. Each group of m_\\sigma equal eigenvalues gives rise to an O(m_\\sigma)-symmetry in configuration space. The combined symmetry group G is a direct product of l+1 such factors, and its cotangent lift has an Ad^*-equivariant Momentum mapping. Regular reduction leads to the Rosochatius system on S^l, which has the same form as the Neumann system albeit for an additional effective potential."},"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":"1205.1834","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-08T21:40:24Z","cross_cats_sorted":["math.SG","nlin.SI"],"title_canon_sha256":"c70ee672e876f17ad62ca6462f02a1fa9b299cf548ae0eb3c14061e35623e830","abstract_canon_sha256":"c55e9b19328e1d95ba91a75f780db57f0af50dfecfd32f8c16f8d815e50772c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:09.888567Z","signature_b64":"mwfAUrE32YacQYdqQa0FmGJKxK3CqYn2MpjFrzcrNMA34Z2v3kPYsap1SW2AiaPv62sbbBeIDyEhhWmvSOzoDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a98ff5a5cb2ceb302a7960e8110c28e7ae5c420adf58417d6e8ea3fe0437d501","last_reissued_at":"2026-05-18T03:20:09.888130Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:09.888130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The degenerate C. Neumann system I: symmetry reduction and convexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG","nlin.SI"],"primary_cat":"math.DS","authors_text":"Heinz Han{\\ss}mann, Holger R. Dullin","submitted_at":"2012-05-08T21:40:24Z","abstract_excerpt":"The C. Neumann system describes a particle on the sphere S^n under the influence of a potential that is a quadratic form. We study the case that the quadratic form has l+1 distinct eigenvalues with multiplicity. Each group of m_\\sigma equal eigenvalues gives rise to an O(m_\\sigma)-symmetry in configuration space. The combined symmetry group G is a direct product of l+1 such factors, and its cotangent lift has an Ad^*-equivariant Momentum mapping. Regular reduction leads to the Rosochatius system on S^l, which has the same form as the Neumann system albeit for an additional effective potential."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1834","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":"1205.1834","created_at":"2026-05-18T03:20:09.888189+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.1834v1","created_at":"2026-05-18T03:20:09.888189+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1834","created_at":"2026-05-18T03:20:09.888189+00:00"},{"alias_kind":"pith_short_12","alias_value":"VGH7LJOLFTVT","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"VGH7LJOLFTVTAKTZ","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"VGH7LJOL","created_at":"2026-05-18T12:27:25.539911+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/VGH7LJOLFTVTAKTZMDUBCDBI46","json":"https://pith.science/pith/VGH7LJOLFTVTAKTZMDUBCDBI46.json","graph_json":"https://pith.science/api/pith-number/VGH7LJOLFTVTAKTZMDUBCDBI46/graph.json","events_json":"https://pith.science/api/pith-number/VGH7LJOLFTVTAKTZMDUBCDBI46/events.json","paper":"https://pith.science/paper/VGH7LJOL"},"agent_actions":{"view_html":"https://pith.science/pith/VGH7LJOLFTVTAKTZMDUBCDBI46","download_json":"https://pith.science/pith/VGH7LJOLFTVTAKTZMDUBCDBI46.json","view_paper":"https://pith.science/paper/VGH7LJOL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.1834&json=true","fetch_graph":"https://pith.science/api/pith-number/VGH7LJOLFTVTAKTZMDUBCDBI46/graph.json","fetch_events":"https://pith.science/api/pith-number/VGH7LJOLFTVTAKTZMDUBCDBI46/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VGH7LJOLFTVTAKTZMDUBCDBI46/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VGH7LJOLFTVTAKTZMDUBCDBI46/action/storage_attestation","attest_author":"https://pith.science/pith/VGH7LJOLFTVTAKTZMDUBCDBI46/action/author_attestation","sign_citation":"https://pith.science/pith/VGH7LJOLFTVTAKTZMDUBCDBI46/action/citation_signature","submit_replication":"https://pith.science/pith/VGH7LJOLFTVTAKTZMDUBCDBI46/action/replication_record"}},"created_at":"2026-05-18T03:20:09.888189+00:00","updated_at":"2026-05-18T03:20:09.888189+00:00"}