{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:6HMCG6U3RZK2XE2SP7YSJJNQZ2","short_pith_number":"pith:6HMCG6U3","canonical_record":{"source":{"id":"1103.4554","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-03-23T15:39:46Z","cross_cats_sorted":["math.MP","nlin.SI"],"title_canon_sha256":"d5b45ece64856145f756799422aac98c4e1a04de3de0990fbefd5482bed9ec72","abstract_canon_sha256":"f09cb150c1a6511620f2df921f292835e6da11d601a23fcd2db123151720beac"},"schema_version":"1.0"},"canonical_sha256":"f1d8237a9b8e55ab93527ff124a5b0ce98eb6c05c908cfd14c39bf2467fa95fe","source":{"kind":"arxiv","id":"1103.4554","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4554","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4554v2","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4554","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"pith_short_12","alias_value":"6HMCG6U3RZK2","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6HMCG6U3RZK2XE2S","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6HMCG6U3","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:6HMCG6U3RZK2XE2SP7YSJJNQZ2","target":"record","payload":{"canonical_record":{"source":{"id":"1103.4554","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-03-23T15:39:46Z","cross_cats_sorted":["math.MP","nlin.SI"],"title_canon_sha256":"d5b45ece64856145f756799422aac98c4e1a04de3de0990fbefd5482bed9ec72","abstract_canon_sha256":"f09cb150c1a6511620f2df921f292835e6da11d601a23fcd2db123151720beac"},"schema_version":"1.0"},"canonical_sha256":"f1d8237a9b8e55ab93527ff124a5b0ce98eb6c05c908cfd14c39bf2467fa95fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:52.602419Z","signature_b64":"VhpssVGkHfz+aWvQAw1DBjoVVmfgCEjsBwY3QHDCLkbSAe6e009CZ2+hNb0KELBaip+DkXmxQJCsHZbCiCfKAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1d8237a9b8e55ab93527ff124a5b0ce98eb6c05c908cfd14c39bf2467fa95fe","last_reissued_at":"2026-05-18T04:21:52.601851Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:52.601851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.4554","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:21:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HWHMgEQc8ghTXb6M3W2LAeSaTDxG+CQ1XI1qa4teUFlNh55cUZar95XesiAj9RKZdM94wGTyNfG9x5Zvl/mfDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:24:55.195077Z"},"content_sha256":"f4d338a58e5df8b43d67393eb70391b3c6ead193d2ccf8fdbdb80de7a748bb28","schema_version":"1.0","event_id":"sha256:f4d338a58e5df8b43d67393eb70391b3c6ead193d2ccf8fdbdb80de7a748bb28"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:6HMCG6U3RZK2XE2SP7YSJJNQZ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the St\\\"ackel Transform","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Alberto Enciso, Angel Ballesteros, Danilo Riglioni, Francisco J. Herranz, Orlando Ragnisco","submitted_at":"2011-03-23T15:39:46Z","abstract_excerpt":"The St\\\"ackel transform is applied to the geodesic motion on Euclidean space, through the harmonic oscillator and Kepler-Coloumb potentials, in order to obtain maximally superintegrable classical systems on N-dimensional Riemannian spaces of nonconstant curvature. By one hand, the harmonic oscillator potential leads to two families of superintegrable systems which are interpreted as an intrinsic Kepler-Coloumb system on a hyperbolic curved space and as the so-called Darboux III oscillator. On the other, the Kepler-Coloumb potential gives rise to an oscillator system on a spherical curved space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4554","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:21:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZHC6e/YRNWCFJIsA+ExN35fPCdO8logyTGkQRTBuBNN5VUBdOQcDVvjfCMUFqJvMzUYE4Haw1MKoa+XSn3FcCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:24:55.195711Z"},"content_sha256":"1ca9d43a3c789f0a3721049a1d13ae558b2e8ea784f7b1fb96c703ec45335eca","schema_version":"1.0","event_id":"sha256:1ca9d43a3c789f0a3721049a1d13ae558b2e8ea784f7b1fb96c703ec45335eca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6HMCG6U3RZK2XE2SP7YSJJNQZ2/bundle.json","state_url":"https://pith.science/pith/6HMCG6U3RZK2XE2SP7YSJJNQZ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6HMCG6U3RZK2XE2SP7YSJJNQZ2/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":"2026-05-27T00:24:55Z","links":{"resolver":"https://pith.science/pith/6HMCG6U3RZK2XE2SP7YSJJNQZ2","bundle":"https://pith.science/pith/6HMCG6U3RZK2XE2SP7YSJJNQZ2/bundle.json","state":"https://pith.science/pith/6HMCG6U3RZK2XE2SP7YSJJNQZ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6HMCG6U3RZK2XE2SP7YSJJNQZ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6HMCG6U3RZK2XE2SP7YSJJNQZ2","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":"f09cb150c1a6511620f2df921f292835e6da11d601a23fcd2db123151720beac","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-03-23T15:39:46Z","title_canon_sha256":"d5b45ece64856145f756799422aac98c4e1a04de3de0990fbefd5482bed9ec72"},"schema_version":"1.0","source":{"id":"1103.4554","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4554","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4554v2","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4554","created_at":"2026-05-18T04:21:52Z"},{"alias_kind":"pith_short_12","alias_value":"6HMCG6U3RZK2","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6HMCG6U3RZK2XE2S","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6HMCG6U3","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:1ca9d43a3c789f0a3721049a1d13ae558b2e8ea784f7b1fb96c703ec45335eca","target":"graph","created_at":"2026-05-18T04:21:52Z","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":"The St\\\"ackel transform is applied to the geodesic motion on Euclidean space, through the harmonic oscillator and Kepler-Coloumb potentials, in order to obtain maximally superintegrable classical systems on N-dimensional Riemannian spaces of nonconstant curvature. By one hand, the harmonic oscillator potential leads to two families of superintegrable systems which are interpreted as an intrinsic Kepler-Coloumb system on a hyperbolic curved space and as the so-called Darboux III oscillator. On the other, the Kepler-Coloumb potential gives rise to an oscillator system on a spherical curved space","authors_text":"Alberto Enciso, Angel Ballesteros, Danilo Riglioni, Francisco J. Herranz, Orlando Ragnisco","cross_cats":["math.MP","nlin.SI"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-03-23T15:39:46Z","title":"Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the St\\\"ackel Transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4554","kind":"arxiv","version":2},"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:f4d338a58e5df8b43d67393eb70391b3c6ead193d2ccf8fdbdb80de7a748bb28","target":"record","created_at":"2026-05-18T04:21:52Z","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":"f09cb150c1a6511620f2df921f292835e6da11d601a23fcd2db123151720beac","cross_cats_sorted":["math.MP","nlin.SI"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2011-03-23T15:39:46Z","title_canon_sha256":"d5b45ece64856145f756799422aac98c4e1a04de3de0990fbefd5482bed9ec72"},"schema_version":"1.0","source":{"id":"1103.4554","kind":"arxiv","version":2}},"canonical_sha256":"f1d8237a9b8e55ab93527ff124a5b0ce98eb6c05c908cfd14c39bf2467fa95fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1d8237a9b8e55ab93527ff124a5b0ce98eb6c05c908cfd14c39bf2467fa95fe","first_computed_at":"2026-05-18T04:21:52.601851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:52.601851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VhpssVGkHfz+aWvQAw1DBjoVVmfgCEjsBwY3QHDCLkbSAe6e009CZ2+hNb0KELBaip+DkXmxQJCsHZbCiCfKAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:52.602419Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4554","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4d338a58e5df8b43d67393eb70391b3c6ead193d2ccf8fdbdb80de7a748bb28","sha256:1ca9d43a3c789f0a3721049a1d13ae558b2e8ea784f7b1fb96c703ec45335eca"],"state_sha256":"714d80e2c7a049ffda0148c2daea746fa193186fea2be8ee8eb4fef29051485b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zVU8AyzOLMwq0UjjuM3EKQDKUcIW4yuxBs4+U9yAIMQygzo6C9n0lLPFfUKJBYCeG6d2kEb43CuNMlAgbaiwBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T00:24:55.199191Z","bundle_sha256":"b36bbf5f0cc477a37009b2e14ac3ce566ee874e9150e7b4a20732ea31c456697"}}