{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HFDDPECK3J3JIFEVNPIIZFEQCM","short_pith_number":"pith:HFDDPECK","canonical_record":{"source":{"id":"1608.07243","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-25T18:30:08Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"cff0dd5857e4dd8f4946dde50fdd176d157c812f4ebec850e0e2b719e987b429","abstract_canon_sha256":"c61310c03758ff06a9e062a751657584591e1766115fcd713bbd5c40d4de7503"},"schema_version":"1.0"},"canonical_sha256":"394637904ada769414956bd08c9490133b142fe6ff540d60248e00b10c9b4a0d","source":{"kind":"arxiv","id":"1608.07243","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07243","created_at":"2026-05-18T00:45:48Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07243v2","created_at":"2026-05-18T00:45:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07243","created_at":"2026-05-18T00:45:48Z"},{"alias_kind":"pith_short_12","alias_value":"HFDDPECK3J3J","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HFDDPECK3J3JIFEV","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HFDDPECK","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HFDDPECK3J3JIFEVNPIIZFEQCM","target":"record","payload":{"canonical_record":{"source":{"id":"1608.07243","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-25T18:30:08Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"cff0dd5857e4dd8f4946dde50fdd176d157c812f4ebec850e0e2b719e987b429","abstract_canon_sha256":"c61310c03758ff06a9e062a751657584591e1766115fcd713bbd5c40d4de7503"},"schema_version":"1.0"},"canonical_sha256":"394637904ada769414956bd08c9490133b142fe6ff540d60248e00b10c9b4a0d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:48.650375Z","signature_b64":"b0OhdUmKXlx4YiYbIwKGbQJ7D6y4PXmUnvm+NXTCIYav5ehL3/WX9Ptw07fFYRFJcVsZQtEZ6usZRx5svhNODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"394637904ada769414956bd08c9490133b142fe6ff540d60248e00b10c9b4a0d","last_reissued_at":"2026-05-18T00:45:48.649790Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:48.649790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.07243","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":"2026-05-18T00:45:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"12jVezzamXayY/pp+nSHDeEd808eQCQBF8vtERrR/08tdF9ONGQnEqBFXttbkrK9W58ytUHK6TxoIhrL1+pmDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:07:22.083241Z"},"content_sha256":"e6ed9daab92b16f273b4c2b17e789a73849317dc10421d682dac3dab75c751c1","schema_version":"1.0","event_id":"sha256:e6ed9daab92b16f273b4c2b17e789a73849317dc10421d682dac3dab75c751c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HFDDPECK3J3JIFEVNPIIZFEQCM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modified Laplace-Beltrami quantization of natural Hamiltonian systems with quadratic constants of motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Claudia Maria Chanu, Giovanni Rastelli, Luca Degiovanni","submitted_at":"2016-08-25T18:30:08Z","abstract_excerpt":"It is natural to investigate if the quantization of an integrable or superintegrable classical Hamiltonian systems is still integrable or superintegrable. We study here this problem in the case of natural Hamiltonians with constants of motion quadratic in the momenta. The procedure of quantization here considered, transforms the Hamiltonian into the Laplace-Beltrami operator plus a scalar potential. In order to transform the constants of motion into symmetry operators of the quantum Hamiltonian, additional scalar potentials, known as quantum corrections, must be introduced, depending on the Ri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07243","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":"2026-05-18T00:45:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B0V8qBkdBuQfWJ0pLNV4ReqNLXC3OExWwQUUE+W0o6PwFHSnONhvwx0TRQKfMjBn28uRDzGvzQkriQ/vqH9MBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:07:22.083938Z"},"content_sha256":"a92348dc335d8124e3b51a9785e11bd488cdf582ae6ae4f9cfcd57a16a187b2b","schema_version":"1.0","event_id":"sha256:a92348dc335d8124e3b51a9785e11bd488cdf582ae6ae4f9cfcd57a16a187b2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HFDDPECK3J3JIFEVNPIIZFEQCM/bundle.json","state_url":"https://pith.science/pith/HFDDPECK3J3JIFEVNPIIZFEQCM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HFDDPECK3J3JIFEVNPIIZFEQCM/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":"2026-06-07T14:07:22Z","links":{"resolver":"https://pith.science/pith/HFDDPECK3J3JIFEVNPIIZFEQCM","bundle":"https://pith.science/pith/HFDDPECK3J3JIFEVNPIIZFEQCM/bundle.json","state":"https://pith.science/pith/HFDDPECK3J3JIFEVNPIIZFEQCM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HFDDPECK3J3JIFEVNPIIZFEQCM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HFDDPECK3J3JIFEVNPIIZFEQCM","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":"c61310c03758ff06a9e062a751657584591e1766115fcd713bbd5c40d4de7503","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-25T18:30:08Z","title_canon_sha256":"cff0dd5857e4dd8f4946dde50fdd176d157c812f4ebec850e0e2b719e987b429"},"schema_version":"1.0","source":{"id":"1608.07243","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07243","created_at":"2026-05-18T00:45:48Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07243v2","created_at":"2026-05-18T00:45:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07243","created_at":"2026-05-18T00:45:48Z"},{"alias_kind":"pith_short_12","alias_value":"HFDDPECK3J3J","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HFDDPECK3J3JIFEV","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HFDDPECK","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:a92348dc335d8124e3b51a9785e11bd488cdf582ae6ae4f9cfcd57a16a187b2b","target":"graph","created_at":"2026-05-18T00:45:48Z","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":"It is natural to investigate if the quantization of an integrable or superintegrable classical Hamiltonian systems is still integrable or superintegrable. We study here this problem in the case of natural Hamiltonians with constants of motion quadratic in the momenta. The procedure of quantization here considered, transforms the Hamiltonian into the Laplace-Beltrami operator plus a scalar potential. In order to transform the constants of motion into symmetry operators of the quantum Hamiltonian, additional scalar potentials, known as quantum corrections, must be introduced, depending on the Ri","authors_text":"Claudia Maria Chanu, Giovanni Rastelli, Luca Degiovanni","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-25T18:30:08Z","title":"Modified Laplace-Beltrami quantization of natural Hamiltonian systems with quadratic constants of motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07243","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:e6ed9daab92b16f273b4c2b17e789a73849317dc10421d682dac3dab75c751c1","target":"record","created_at":"2026-05-18T00:45:48Z","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":"c61310c03758ff06a9e062a751657584591e1766115fcd713bbd5c40d4de7503","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-25T18:30:08Z","title_canon_sha256":"cff0dd5857e4dd8f4946dde50fdd176d157c812f4ebec850e0e2b719e987b429"},"schema_version":"1.0","source":{"id":"1608.07243","kind":"arxiv","version":2}},"canonical_sha256":"394637904ada769414956bd08c9490133b142fe6ff540d60248e00b10c9b4a0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"394637904ada769414956bd08c9490133b142fe6ff540d60248e00b10c9b4a0d","first_computed_at":"2026-05-18T00:45:48.649790Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:48.649790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b0OhdUmKXlx4YiYbIwKGbQJ7D6y4PXmUnvm+NXTCIYav5ehL3/WX9Ptw07fFYRFJcVsZQtEZ6usZRx5svhNODw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:48.650375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.07243","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6ed9daab92b16f273b4c2b17e789a73849317dc10421d682dac3dab75c751c1","sha256:a92348dc335d8124e3b51a9785e11bd488cdf582ae6ae4f9cfcd57a16a187b2b"],"state_sha256":"2c81505423769567cb3ad06f7344c85a444cadd0aa74aae3e11e045e574c7ce1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F2Dz9ldoRB9+QjQYaMEzjvopFUDcATFEAr5FuZ7lQcbkw655wRM3JamtcQLW2CLZZZED4rMJHDnmskomxgI+Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T14:07:22.087782Z","bundle_sha256":"bc76bb4bccc1d6e95b5b115315d54743fb545280e6a4a54a4dd9e3a72b150d63"}}