{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:EKK2LDWZ234TE6EV3ODW6SIB3Y","short_pith_number":"pith:EKK2LDWZ","schema_version":"1.0","canonical_sha256":"2295a58ed9d6f9327895db876f4901de1a8c1c79de30052c64fe169fb59eb938","source":{"kind":"arxiv","id":"1504.00760","version":2},"attestation_state":"computed","paper":{"title":"Runge-Lenz vector in Calogero-Coulomb problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI","quant-ph"],"primary_cat":"hep-th","authors_text":"Armen Nersessian, Tigran Hakobyan","submitted_at":"2015-04-03T07:23:50Z","abstract_excerpt":"We construct the Runge-Lenz vector and symmetry algebra of rational Calogero-Coulomb problem, formulated in terms of Dunkl operators. We find that they are proper deformations of their Coulomb counterpart. Together with similar correspondence between the Calogero-oscillator and oscillator models, this observation permits to claim that most of properties of Coulomb and oscillator systems can be lifted to their Calogero-extended analogs by the proper replacement of momenta by Dunkl momenta operators."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1504.00760","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-04-03T07:23:50Z","cross_cats_sorted":["math-ph","math.MP","nlin.SI","quant-ph"],"title_canon_sha256":"c38223ebe21950a83677f7a8b2c766e26977b8f83fc3d8a147af24ff290fa371","abstract_canon_sha256":"fdb29603e8edf507a6cfabf13e3e3c99e2e5d0143f13186c718b77431db745b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:10.641454Z","signature_b64":"eHyzA6imo0iJIKUb+PRHpan8gdVjG+uHH7c9nrhhmpcikayXaNtvmOF4UJxuq0z7MBxOc92scyG6HN7l/mBzBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2295a58ed9d6f9327895db876f4901de1a8c1c79de30052c64fe169fb59eb938","last_reissued_at":"2026-05-18T01:35:10.640698Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:10.640698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Runge-Lenz vector in Calogero-Coulomb problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI","quant-ph"],"primary_cat":"hep-th","authors_text":"Armen Nersessian, Tigran Hakobyan","submitted_at":"2015-04-03T07:23:50Z","abstract_excerpt":"We construct the Runge-Lenz vector and symmetry algebra of rational Calogero-Coulomb problem, formulated in terms of Dunkl operators. We find that they are proper deformations of their Coulomb counterpart. Together with similar correspondence between the Calogero-oscillator and oscillator models, this observation permits to claim that most of properties of Coulomb and oscillator systems can be lifted to their Calogero-extended analogs by the proper replacement of momenta by Dunkl momenta operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00760","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1504.00760","created_at":"2026-05-18T01:35:10.640829+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.00760v2","created_at":"2026-05-18T01:35:10.640829+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00760","created_at":"2026-05-18T01:35:10.640829+00:00"},{"alias_kind":"pith_short_12","alias_value":"EKK2LDWZ234T","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"EKK2LDWZ234TE6EV","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"EKK2LDWZ","created_at":"2026-05-18T12:29:19.899920+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EKK2LDWZ234TE6EV3ODW6SIB3Y","json":"https://pith.science/pith/EKK2LDWZ234TE6EV3ODW6SIB3Y.json","graph_json":"https://pith.science/api/pith-number/EKK2LDWZ234TE6EV3ODW6SIB3Y/graph.json","events_json":"https://pith.science/api/pith-number/EKK2LDWZ234TE6EV3ODW6SIB3Y/events.json","paper":"https://pith.science/paper/EKK2LDWZ"},"agent_actions":{"view_html":"https://pith.science/pith/EKK2LDWZ234TE6EV3ODW6SIB3Y","download_json":"https://pith.science/pith/EKK2LDWZ234TE6EV3ODW6SIB3Y.json","view_paper":"https://pith.science/paper/EKK2LDWZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.00760&json=true","fetch_graph":"https://pith.science/api/pith-number/EKK2LDWZ234TE6EV3ODW6SIB3Y/graph.json","fetch_events":"https://pith.science/api/pith-number/EKK2LDWZ234TE6EV3ODW6SIB3Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EKK2LDWZ234TE6EV3ODW6SIB3Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EKK2LDWZ234TE6EV3ODW6SIB3Y/action/storage_attestation","attest_author":"https://pith.science/pith/EKK2LDWZ234TE6EV3ODW6SIB3Y/action/author_attestation","sign_citation":"https://pith.science/pith/EKK2LDWZ234TE6EV3ODW6SIB3Y/action/citation_signature","submit_replication":"https://pith.science/pith/EKK2LDWZ234TE6EV3ODW6SIB3Y/action/replication_record"}},"created_at":"2026-05-18T01:35:10.640829+00:00","updated_at":"2026-05-18T01:35:10.640829+00:00"}