{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:UI4TKUB3QSMTXQBMB7YGTRWGHS","short_pith_number":"pith:UI4TKUB3","canonical_record":{"source":{"id":"0912.3158","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-12-16T15:07:27Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"e31f82b273acfa27b9919f2d29c2ab7eb92dff9880c596319b4a9c83903ce315","abstract_canon_sha256":"426a3dfca7949f7f390f1bbe57ee516dc998e65a42e5691c280e68c2a258f721"},"schema_version":"1.0"},"canonical_sha256":"a23935503b84993bc02c0ff069c6c63ca6f231143358ac7f3bc33f5bf24f9e46","source":{"kind":"arxiv","id":"0912.3158","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.3158","created_at":"2026-05-18T02:10:16Z"},{"alias_kind":"arxiv_version","alias_value":"0912.3158v1","created_at":"2026-05-18T02:10:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.3158","created_at":"2026-05-18T02:10:16Z"},{"alias_kind":"pith_short_12","alias_value":"UI4TKUB3QSMT","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"UI4TKUB3QSMTXQBM","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"UI4TKUB3","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:UI4TKUB3QSMTXQBMB7YGTRWGHS","target":"record","payload":{"canonical_record":{"source":{"id":"0912.3158","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-12-16T15:07:27Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"e31f82b273acfa27b9919f2d29c2ab7eb92dff9880c596319b4a9c83903ce315","abstract_canon_sha256":"426a3dfca7949f7f390f1bbe57ee516dc998e65a42e5691c280e68c2a258f721"},"schema_version":"1.0"},"canonical_sha256":"a23935503b84993bc02c0ff069c6c63ca6f231143358ac7f3bc33f5bf24f9e46","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:16.556869Z","signature_b64":"zD4cdfQ7cwJ/MasB8sA6LF+6DMg4cDsPbzjRkTB8eATnQffJJ72iWGssD5v98V8cnckB4ENRThDQZgwsdR0CBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a23935503b84993bc02c0ff069c6c63ca6f231143358ac7f3bc33f5bf24f9e46","last_reissued_at":"2026-05-18T02:10:16.556038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:16.556038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.3158","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:10:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bADMJbqEfc/UK0dKhOKCH6nsyJm2IwHu8v2I3rjuEQSC/ZJnxDVsTta6kccthGTNjBuMO0gLtmhP1bL1h7pRBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T13:36:49.071279Z"},"content_sha256":"71dc41a7a684ea78fc7fbc227f20d9ece124a5df17309376ab147c3b54ecbec5","schema_version":"1.0","event_id":"sha256:71dc41a7a684ea78fc7fbc227f20d9ece124a5df17309376ab147c3b54ecbec5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:UI4TKUB3QSMTXQBMB7YGTRWGHS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Families of classical subgroup separable superintegrable systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"E.G. Kalnins, J. M.Kress, W. Miller Jr","submitted_at":"2009-12-16T15:07:27Z","abstract_excerpt":"We describe a method for determining a complete set of integrals for a classical Hamiltonian that separates in orthogonal subgroup coordinates. As examples, we use it to determine complete sets of integrals, polynomial in the momenta, for some families of generalized oscillator and Kepler-Coulomb systems, hence demonstrating their superintegrability. The latter generalizes recent results of Verrier and Evans, and Rodriguez, Tempesta and Winternitz. Another example is given of a superintegrable system on a non-conformally flat space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.3158","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:10:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OZquEhw9Q0u1oP/FCXVhiQDkGdj7OuEkg+x/MDw+SpZxkGM70JP5R9nW3jN9rYL8O0gqBsaMdsVwx6Afmbm6Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T13:36:49.071640Z"},"content_sha256":"7183e4b6a2a45145187643caa83a4f10af7ec8baf0d554335b37fa748086d442","schema_version":"1.0","event_id":"sha256:7183e4b6a2a45145187643caa83a4f10af7ec8baf0d554335b37fa748086d442"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UI4TKUB3QSMTXQBMB7YGTRWGHS/bundle.json","state_url":"https://pith.science/pith/UI4TKUB3QSMTXQBMB7YGTRWGHS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UI4TKUB3QSMTXQBMB7YGTRWGHS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T13:36:49Z","links":{"resolver":"https://pith.science/pith/UI4TKUB3QSMTXQBMB7YGTRWGHS","bundle":"https://pith.science/pith/UI4TKUB3QSMTXQBMB7YGTRWGHS/bundle.json","state":"https://pith.science/pith/UI4TKUB3QSMTXQBMB7YGTRWGHS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UI4TKUB3QSMTXQBMB7YGTRWGHS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:UI4TKUB3QSMTXQBMB7YGTRWGHS","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":"426a3dfca7949f7f390f1bbe57ee516dc998e65a42e5691c280e68c2a258f721","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-12-16T15:07:27Z","title_canon_sha256":"e31f82b273acfa27b9919f2d29c2ab7eb92dff9880c596319b4a9c83903ce315"},"schema_version":"1.0","source":{"id":"0912.3158","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.3158","created_at":"2026-05-18T02:10:16Z"},{"alias_kind":"arxiv_version","alias_value":"0912.3158v1","created_at":"2026-05-18T02:10:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.3158","created_at":"2026-05-18T02:10:16Z"},{"alias_kind":"pith_short_12","alias_value":"UI4TKUB3QSMT","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"UI4TKUB3QSMTXQBM","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"UI4TKUB3","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:7183e4b6a2a45145187643caa83a4f10af7ec8baf0d554335b37fa748086d442","target":"graph","created_at":"2026-05-18T02:10:16Z","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":"We describe a method for determining a complete set of integrals for a classical Hamiltonian that separates in orthogonal subgroup coordinates. As examples, we use it to determine complete sets of integrals, polynomial in the momenta, for some families of generalized oscillator and Kepler-Coulomb systems, hence demonstrating their superintegrability. The latter generalizes recent results of Verrier and Evans, and Rodriguez, Tempesta and Winternitz. Another example is given of a superintegrable system on a non-conformally flat space.","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":"2009-12-16T15:07:27Z","title":"Families of classical subgroup separable superintegrable systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.3158","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":"sha256:71dc41a7a684ea78fc7fbc227f20d9ece124a5df17309376ab147c3b54ecbec5","target":"record","created_at":"2026-05-18T02:10:16Z","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":"426a3dfca7949f7f390f1bbe57ee516dc998e65a42e5691c280e68c2a258f721","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-12-16T15:07:27Z","title_canon_sha256":"e31f82b273acfa27b9919f2d29c2ab7eb92dff9880c596319b4a9c83903ce315"},"schema_version":"1.0","source":{"id":"0912.3158","kind":"arxiv","version":1}},"canonical_sha256":"a23935503b84993bc02c0ff069c6c63ca6f231143358ac7f3bc33f5bf24f9e46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a23935503b84993bc02c0ff069c6c63ca6f231143358ac7f3bc33f5bf24f9e46","first_computed_at":"2026-05-18T02:10:16.556038Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:10:16.556038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zD4cdfQ7cwJ/MasB8sA6LF+6DMg4cDsPbzjRkTB8eATnQffJJ72iWGssD5v98V8cnckB4ENRThDQZgwsdR0CBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:10:16.556869Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.3158","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71dc41a7a684ea78fc7fbc227f20d9ece124a5df17309376ab147c3b54ecbec5","sha256:7183e4b6a2a45145187643caa83a4f10af7ec8baf0d554335b37fa748086d442"],"state_sha256":"d09827e7bda48ba14449cac325945c7e05435b5709015ab9299a8b745fec3bde"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lv9EIOhnu7YwvCuSB7Ig0s8PFBhZjrmeOMU1wqalPvx9XoLaSX5ERSKDz8/7hhHAw5eSHjKjyw8WQh3KWlKgAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T13:36:49.073647Z","bundle_sha256":"af36ba2bf5acbbd5cf4270af33c3f99b52d06c8e98918630700769045e5e44ee"}}