{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:JIAB3PMTYYOEU5EBO6OGD5YWQF","short_pith_number":"pith:JIAB3PMT","canonical_record":{"source":{"id":"math-ph/0501035","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-01-12T14:15:02Z","cross_cats_sorted":["math.MP","nlin.SI"],"title_canon_sha256":"d8cecf1f86308069377f00540c72ae8bd51391eee8afe037e29ab1f36cc483ce","abstract_canon_sha256":"a7cc6b14b4d6331c5d5d7f4d02886556f22c20f073c7977992fe98d0455a0051"},"schema_version":"1.0"},"canonical_sha256":"4a001dbd93c61c4a7481779c61f71681430eeea4b9b0bae0d5bffea580275927","source":{"kind":"arxiv","id":"math-ph/0501035","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0501035","created_at":"2026-05-17T23:40:37Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0501035v1","created_at":"2026-05-17T23:40:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0501035","created_at":"2026-05-17T23:40:37Z"},{"alias_kind":"pith_short_12","alias_value":"JIAB3PMTYYOE","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"JIAB3PMTYYOEU5EB","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"JIAB3PMT","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:JIAB3PMTYYOEU5EBO6OGD5YWQF","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0501035","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-01-12T14:15:02Z","cross_cats_sorted":["math.MP","nlin.SI"],"title_canon_sha256":"d8cecf1f86308069377f00540c72ae8bd51391eee8afe037e29ab1f36cc483ce","abstract_canon_sha256":"a7cc6b14b4d6331c5d5d7f4d02886556f22c20f073c7977992fe98d0455a0051"},"schema_version":"1.0"},"canonical_sha256":"4a001dbd93c61c4a7481779c61f71681430eeea4b9b0bae0d5bffea580275927","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:37.197846Z","signature_b64":"7ORGr6RM2t0Yy0gLLQ6U86GQh7UgZBMjNg20/DX3FBfYVO//Lw4ST2XKyb9usxoIuJoSY61RnI7JSDNul436CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a001dbd93c61c4a7481779c61f71681430eeea4b9b0bae0d5bffea580275927","last_reissued_at":"2026-05-17T23:40:37.197001Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:37.197001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0501035","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":"2026-05-17T23:40:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/A9g5gMc3yrcA7m7Aeh78BDLeNIZOmByhlgiL2whB3Pxvtqj3cdesG2cvN9G9W4SlML39WhB93AWnbIpjR3xBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:07:25.197789Z"},"content_sha256":"ca68436af032a0c030af9343b559981d06189ba44c6f39139c3c8e7004679d4b","schema_version":"1.0","event_id":"sha256:ca68436af032a0c030af9343b559981d06189ba44c6f39139c3c8e7004679d4b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:JIAB3PMTYYOEU5EBO6OGD5YWQF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximally superintegrable Smorodinsky-Winternitz systems on the N-dimensional sphere and hyperbolic spaces","license":"","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Angel Ballesteros, Francisco J. Herranz, Mariano Santander, Teresa Sanz-Gil","submitted_at":"2005-01-12T14:15:02Z","abstract_excerpt":"The classical Smorodinsky-Winternitz systems on the ND sphere, Euclidean and hyperbolic spaces S^N, E^N and H^N are simultaneously approached starting from the Lie algebras so_k(N+1), which include a parametric dependence on the curvature k. General expressions for the Hamiltonian and its integrals of motion are given in terms of intrinsic geodesic coordinate systems. Each Lie algebra generator gives rise to an integral of motion, so that a set of N(N+1)/2 integrals is obtained. Furthermore, 2N-1 functionally independent ones are identified which, in turn, shows that the well known maximal sup"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0501035","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":"2026-05-17T23:40:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y8ZCvs7yEYSa4iVBg9DMJfB8iSy0Wdl+dz0W5iHMRtpY6eVne+vzUpTol65dumsngqq3BWp2wX8nT2843afyCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:07:25.198421Z"},"content_sha256":"8f02ecd8590e9b7fcb683994420feb798073d4c33421ceefed9f61ffc68f9b18","schema_version":"1.0","event_id":"sha256:8f02ecd8590e9b7fcb683994420feb798073d4c33421ceefed9f61ffc68f9b18"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JIAB3PMTYYOEU5EBO6OGD5YWQF/bundle.json","state_url":"https://pith.science/pith/JIAB3PMTYYOEU5EBO6OGD5YWQF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JIAB3PMTYYOEU5EBO6OGD5YWQF/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":"2026-05-30T05:07:25Z","links":{"resolver":"https://pith.science/pith/JIAB3PMTYYOEU5EBO6OGD5YWQF","bundle":"https://pith.science/pith/JIAB3PMTYYOEU5EBO6OGD5YWQF/bundle.json","state":"https://pith.science/pith/JIAB3PMTYYOEU5EBO6OGD5YWQF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JIAB3PMTYYOEU5EBO6OGD5YWQF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:JIAB3PMTYYOEU5EBO6OGD5YWQF","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":"a7cc6b14b4d6331c5d5d7f4d02886556f22c20f073c7977992fe98d0455a0051","cross_cats_sorted":["math.MP","nlin.SI"],"license":"","primary_cat":"math-ph","submitted_at":"2005-01-12T14:15:02Z","title_canon_sha256":"d8cecf1f86308069377f00540c72ae8bd51391eee8afe037e29ab1f36cc483ce"},"schema_version":"1.0","source":{"id":"math-ph/0501035","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0501035","created_at":"2026-05-17T23:40:37Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0501035v1","created_at":"2026-05-17T23:40:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0501035","created_at":"2026-05-17T23:40:37Z"},{"alias_kind":"pith_short_12","alias_value":"JIAB3PMTYYOE","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"JIAB3PMTYYOEU5EB","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"JIAB3PMT","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:8f02ecd8590e9b7fcb683994420feb798073d4c33421ceefed9f61ffc68f9b18","target":"graph","created_at":"2026-05-17T23:40:37Z","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 classical Smorodinsky-Winternitz systems on the ND sphere, Euclidean and hyperbolic spaces S^N, E^N and H^N are simultaneously approached starting from the Lie algebras so_k(N+1), which include a parametric dependence on the curvature k. General expressions for the Hamiltonian and its integrals of motion are given in terms of intrinsic geodesic coordinate systems. Each Lie algebra generator gives rise to an integral of motion, so that a set of N(N+1)/2 integrals is obtained. Furthermore, 2N-1 functionally independent ones are identified which, in turn, shows that the well known maximal sup","authors_text":"Angel Ballesteros, Francisco J. Herranz, Mariano Santander, Teresa Sanz-Gil","cross_cats":["math.MP","nlin.SI"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2005-01-12T14:15:02Z","title":"Maximally superintegrable Smorodinsky-Winternitz systems on the N-dimensional sphere and hyperbolic spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0501035","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:ca68436af032a0c030af9343b559981d06189ba44c6f39139c3c8e7004679d4b","target":"record","created_at":"2026-05-17T23:40:37Z","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":"a7cc6b14b4d6331c5d5d7f4d02886556f22c20f073c7977992fe98d0455a0051","cross_cats_sorted":["math.MP","nlin.SI"],"license":"","primary_cat":"math-ph","submitted_at":"2005-01-12T14:15:02Z","title_canon_sha256":"d8cecf1f86308069377f00540c72ae8bd51391eee8afe037e29ab1f36cc483ce"},"schema_version":"1.0","source":{"id":"math-ph/0501035","kind":"arxiv","version":1}},"canonical_sha256":"4a001dbd93c61c4a7481779c61f71681430eeea4b9b0bae0d5bffea580275927","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a001dbd93c61c4a7481779c61f71681430eeea4b9b0bae0d5bffea580275927","first_computed_at":"2026-05-17T23:40:37.197001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:37.197001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7ORGr6RM2t0Yy0gLLQ6U86GQh7UgZBMjNg20/DX3FBfYVO//Lw4ST2XKyb9usxoIuJoSY61RnI7JSDNul436CQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:37.197846Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0501035","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca68436af032a0c030af9343b559981d06189ba44c6f39139c3c8e7004679d4b","sha256:8f02ecd8590e9b7fcb683994420feb798073d4c33421ceefed9f61ffc68f9b18"],"state_sha256":"8dd3e1b9a04d30d4902554d430c1851ac3d032f05e717e1bc0d698ddba6a3aec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yKGjjjtwO2Cl6XcL+E9k9BmCjE8Tj/3YWgrMTR7no3Ee75cJ4ICApYmLw60QXLD/mvgkhUmE6ZT2PeTejQ/SDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:07:25.201588Z","bundle_sha256":"c5c2a6156377edd4e58a4110ec6b56269ec02a6bfa3ca6197d7b42caea2ce1d8"}}