{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3TRGA3HTJ3HN7QSAJIS3EXLPSJ","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":"656355b78a8b6fc2fe57d819776e0948754b9ab1f1d184a665a282ed96e6b27a","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-11-07T05:20:26Z","title_canon_sha256":"78d631e0bd3155c655d3d353c9cef02afbcccbf9a1f13d1d6f7dbb77ecc77294"},"schema_version":"1.0","source":{"id":"1211.1452","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1452","created_at":"2026-05-18T02:49:52Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1452v1","created_at":"2026-05-18T02:49:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1452","created_at":"2026-05-18T02:49:52Z"},{"alias_kind":"pith_short_12","alias_value":"3TRGA3HTJ3HN","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3TRGA3HTJ3HN7QSA","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3TRGA3HT","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:d29d1cc0caf6b78f328ce0358bfc2484edb338ca98ecd4f91c63a787cc05e4c3","target":"graph","created_at":"2026-05-18T02:49:52Z","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"},"paper":{"abstract_excerpt":"Superintegrable systems in two- and three-dimensional spaces of constant curvature have been extensively studied. From these, superintegrable systems in conformally flat spaces can be constructed by Staeckel transform. In this paper a method developed to establish the superintegrability of the Tremblay-Turbiner-Winternitz system in two dimensions is extended to higher dimensions and a superintegrable system on a non-conformally-flat four-dimensional space is found. In doing so, curvature corrections to the corresponding classical potential are found to be necessary. It is found that some subal","authors_text":"E. G. Kalnins, J. M. Kress, W. Miller Jr","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-11-07T05:20:26Z","title":"Superintegrability in a non-conformally-flat space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1452","kind":"arxiv","version":1},"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:a65e76690a7fdc79de18093554a5fd900602c214ecdff88a372494c113f400ca","target":"record","created_at":"2026-05-18T02:49:52Z","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":"656355b78a8b6fc2fe57d819776e0948754b9ab1f1d184a665a282ed96e6b27a","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-11-07T05:20:26Z","title_canon_sha256":"78d631e0bd3155c655d3d353c9cef02afbcccbf9a1f13d1d6f7dbb77ecc77294"},"schema_version":"1.0","source":{"id":"1211.1452","kind":"arxiv","version":1}},"canonical_sha256":"dce2606cf34ecedfc2404a25b25d6f925950a3718a1267292507d0201e2050d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dce2606cf34ecedfc2404a25b25d6f925950a3718a1267292507d0201e2050d7","first_computed_at":"2026-05-18T02:49:52.402285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:52.402285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U0hNCsAHwFkIhCs6Gm0NGSgi5UPMHhGmYfkat39/8+zrBGp1Df+YxaUrfZ2r4ezHJixIukGW/7GqHtrNpTSQCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:52.402789Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1452","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a65e76690a7fdc79de18093554a5fd900602c214ecdff88a372494c113f400ca","sha256:d29d1cc0caf6b78f328ce0358bfc2484edb338ca98ecd4f91c63a787cc05e4c3"],"state_sha256":"0824ea9c6672e6e8f0047dd0b2a5d9bbc21ae584d0901c286926ca7a9be896b5"}