{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:RLWBDT37M5RJC7S4EINVGTITVV","short_pith_number":"pith:RLWBDT37","canonical_record":{"source":{"id":"1509.01077","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-03T13:34:02Z","cross_cats_sorted":["cond-mat.str-el","hep-th","math.MP","nlin.SI","quant-ph"],"title_canon_sha256":"d439c8e1cf2d669df86b5ce7931b9627eae6f0395123f849e40cc7bacb0577ea","abstract_canon_sha256":"d7cdb41caf6553fa4c1582e68a8be50005ee104dd1cf4e5930cc663eb6c473bd"},"schema_version":"1.0"},"canonical_sha256":"8aec11cf7f6762917e5c221b534d13ad77cfa4c952f16b5d044a3cd10c026d35","source":{"kind":"arxiv","id":"1509.01077","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01077","created_at":"2026-05-18T01:20:01Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01077v2","created_at":"2026-05-18T01:20:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01077","created_at":"2026-05-18T01:20:01Z"},{"alias_kind":"pith_short_12","alias_value":"RLWBDT37M5RJ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RLWBDT37M5RJC7S4","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RLWBDT37","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:RLWBDT37M5RJC7S4EINVGTITVV","target":"record","payload":{"canonical_record":{"source":{"id":"1509.01077","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-03T13:34:02Z","cross_cats_sorted":["cond-mat.str-el","hep-th","math.MP","nlin.SI","quant-ph"],"title_canon_sha256":"d439c8e1cf2d669df86b5ce7931b9627eae6f0395123f849e40cc7bacb0577ea","abstract_canon_sha256":"d7cdb41caf6553fa4c1582e68a8be50005ee104dd1cf4e5930cc663eb6c473bd"},"schema_version":"1.0"},"canonical_sha256":"8aec11cf7f6762917e5c221b534d13ad77cfa4c952f16b5d044a3cd10c026d35","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:01.412689Z","signature_b64":"7y9QrLLnRFKnMpfsGp4JMDxPYHKsCRrBZG86nZ+LYHPnfTrb350lRuN8vJMoyMscKxrnKu9KJHKMO1hyERgjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8aec11cf7f6762917e5c221b534d13ad77cfa4c952f16b5d044a3cd10c026d35","last_reissued_at":"2026-05-18T01:20:01.412024Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:01.412024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.01077","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":"2026-05-18T01:20:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gio4hcUP5aKprmA3lQKa/vQF9KBiAZwr7fXnZtbUcxRy0DbTnzABXXWsC4Au3ByaMWgtxvxkuRsMFoIEottPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:39:32.196963Z"},"content_sha256":"c845435e14654ddd3c1f9aa91a49fea4ba076df8a8c5b0bdb2be92bc2ab7f2c8","schema_version":"1.0","event_id":"sha256:c845435e14654ddd3c1f9aa91a49fea4ba076df8a8c5b0bdb2be92bc2ab7f2c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:RLWBDT37M5RJC7S4EINVGTITVV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Integrability and separation of variables in Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","hep-th","math.MP","nlin.SI","quant-ph"],"primary_cat":"math-ph","authors_text":"Armen Nersessian, Tigran Hakobyan","submitted_at":"2015-09-03T13:34:02Z","abstract_excerpt":"We propose the integrable N-dimensional Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems and construct their constants of motion via the Dunkl operators. Their Schr\\\"odinger equations decouple in parabolic and elliptic coordinates into the set of three differential equations like for the Coulomb-Stark and two-center Coulomb problems. The Calogero term preserves the energy levels, but changes their degrees of degeneracy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01077","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":"2026-05-18T01:20:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O6tO6IHxvrJGXhc2JsBJaQ4wg1qTUoakZ8jfRDlXZ0mLFqYA/xn8ln32ukJuk8zVqBev9+XqPabHcxnMV/PZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:39:32.197335Z"},"content_sha256":"1a9d21f3956f87287f606f938fbc2deead6a3d5f4a343526effb9456c8b29806","schema_version":"1.0","event_id":"sha256:1a9d21f3956f87287f606f938fbc2deead6a3d5f4a343526effb9456c8b29806"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RLWBDT37M5RJC7S4EINVGTITVV/bundle.json","state_url":"https://pith.science/pith/RLWBDT37M5RJC7S4EINVGTITVV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RLWBDT37M5RJC7S4EINVGTITVV/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":"2026-06-03T18:39:32Z","links":{"resolver":"https://pith.science/pith/RLWBDT37M5RJC7S4EINVGTITVV","bundle":"https://pith.science/pith/RLWBDT37M5RJC7S4EINVGTITVV/bundle.json","state":"https://pith.science/pith/RLWBDT37M5RJC7S4EINVGTITVV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RLWBDT37M5RJC7S4EINVGTITVV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RLWBDT37M5RJC7S4EINVGTITVV","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":"d7cdb41caf6553fa4c1582e68a8be50005ee104dd1cf4e5930cc663eb6c473bd","cross_cats_sorted":["cond-mat.str-el","hep-th","math.MP","nlin.SI","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-03T13:34:02Z","title_canon_sha256":"d439c8e1cf2d669df86b5ce7931b9627eae6f0395123f849e40cc7bacb0577ea"},"schema_version":"1.0","source":{"id":"1509.01077","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01077","created_at":"2026-05-18T01:20:01Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01077v2","created_at":"2026-05-18T01:20:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01077","created_at":"2026-05-18T01:20:01Z"},{"alias_kind":"pith_short_12","alias_value":"RLWBDT37M5RJ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RLWBDT37M5RJC7S4","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RLWBDT37","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:1a9d21f3956f87287f606f938fbc2deead6a3d5f4a343526effb9456c8b29806","target":"graph","created_at":"2026-05-18T01:20:01Z","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 propose the integrable N-dimensional Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems and construct their constants of motion via the Dunkl operators. Their Schr\\\"odinger equations decouple in parabolic and elliptic coordinates into the set of three differential equations like for the Coulomb-Stark and two-center Coulomb problems. The Calogero term preserves the energy levels, but changes their degrees of degeneracy.","authors_text":"Armen Nersessian, Tigran Hakobyan","cross_cats":["cond-mat.str-el","hep-th","math.MP","nlin.SI","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-03T13:34:02Z","title":"Integrability and separation of variables in Calogero-Coulomb-Stark and two-center Calogero-Coulomb systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01077","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:c845435e14654ddd3c1f9aa91a49fea4ba076df8a8c5b0bdb2be92bc2ab7f2c8","target":"record","created_at":"2026-05-18T01:20:01Z","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":"d7cdb41caf6553fa4c1582e68a8be50005ee104dd1cf4e5930cc663eb6c473bd","cross_cats_sorted":["cond-mat.str-el","hep-th","math.MP","nlin.SI","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-09-03T13:34:02Z","title_canon_sha256":"d439c8e1cf2d669df86b5ce7931b9627eae6f0395123f849e40cc7bacb0577ea"},"schema_version":"1.0","source":{"id":"1509.01077","kind":"arxiv","version":2}},"canonical_sha256":"8aec11cf7f6762917e5c221b534d13ad77cfa4c952f16b5d044a3cd10c026d35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8aec11cf7f6762917e5c221b534d13ad77cfa4c952f16b5d044a3cd10c026d35","first_computed_at":"2026-05-18T01:20:01.412024Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:01.412024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7y9QrLLnRFKnMpfsGp4JMDxPYHKsCRrBZG86nZ+LYHPnfTrb350lRuN8vJMoyMscKxrnKu9KJHKMO1hyERgjBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:01.412689Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01077","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c845435e14654ddd3c1f9aa91a49fea4ba076df8a8c5b0bdb2be92bc2ab7f2c8","sha256:1a9d21f3956f87287f606f938fbc2deead6a3d5f4a343526effb9456c8b29806"],"state_sha256":"204be1c0c6b1b7a6f216d91deafe75f8d3808a7c8b5a30409edbf1314df4bdfa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hcpgLilrcBcn7ABU/D6eRq2DyHgoB3Itqbwyv1BLu/+lkBS/R5sBKidd/r4KIQx5QKUthlA5lp7Cpg0yMyXKAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:39:32.199395Z","bundle_sha256":"05f17dc6018c373037521a9ac9607867cdf2cc8b48ca2d8c5cfeb18c82b7bc6a"}}