{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:GLRPULGUK34WBEWEX4NHCGAXI7","short_pith_number":"pith:GLRPULGU","schema_version":"1.0","canonical_sha256":"32e2fa2cd456f96092c4bf1a71181747eb1ee723ae8adfcd15b97655336b6835","source":{"kind":"arxiv","id":"2412.16733","version":2},"attestation_state":"computed","paper":{"title":"Spherical to Cartesian Coordinates Transformation for Solid Harmonics Revisited","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","physics.atm-clus","physics.chem-ph","physics.comp-ph"],"primary_cat":"cond-mat.other","authors_text":"Chiara Ribaldone, Jacques Kontak Desmarais","submitted_at":"2024-12-21T18:53:41Z","abstract_excerpt":"Spherical Harmonic Gaussian type orbitals and Slater functions can be expressed using spherical coordinates or a linear combinations of the appropriate Cartesian functions. General expressions for the transformation coefficients between the two representations are provided. Values for the transformation coefficients are tabulated up to the quantum number $\\ell = 10$. The formula is applied to construct the Hartree potential by an arbitrary-order multipole expansion."},"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":"2412.16733","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.other","submitted_at":"2024-12-21T18:53:41Z","cross_cats_sorted":["cond-mat.mtrl-sci","physics.atm-clus","physics.chem-ph","physics.comp-ph"],"title_canon_sha256":"25ac5b2ffc41a47040613a5dd3ab32532d654e981e196710f0091b14029f064c","abstract_canon_sha256":"0bcac78b1ccd78de76999185711f15da0bf514fc54e246114dd85e5dd2781576"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:39:06.045210Z","signature_b64":"3wsvBODPu2XUthj8c30G9GAI2qhUo5ikmwNhn2udT/CpRPrPX6pP9j/QDOsKSbN9wQZMIe7PoetsnMSLoE33DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32e2fa2cd456f96092c4bf1a71181747eb1ee723ae8adfcd15b97655336b6835","last_reissued_at":"2026-07-05T11:39:06.044708Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:39:06.044708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spherical to Cartesian Coordinates Transformation for Solid Harmonics Revisited","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","physics.atm-clus","physics.chem-ph","physics.comp-ph"],"primary_cat":"cond-mat.other","authors_text":"Chiara Ribaldone, Jacques Kontak Desmarais","submitted_at":"2024-12-21T18:53:41Z","abstract_excerpt":"Spherical Harmonic Gaussian type orbitals and Slater functions can be expressed using spherical coordinates or a linear combinations of the appropriate Cartesian functions. General expressions for the transformation coefficients between the two representations are provided. Values for the transformation coefficients are tabulated up to the quantum number $\\ell = 10$. The formula is applied to construct the Hartree potential by an arbitrary-order multipole expansion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.16733","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.16733/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2412.16733","created_at":"2026-07-05T11:39:06.044762+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.16733v2","created_at":"2026-07-05T11:39:06.044762+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.16733","created_at":"2026-07-05T11:39:06.044762+00:00"},{"alias_kind":"pith_short_12","alias_value":"GLRPULGUK34W","created_at":"2026-07-05T11:39:06.044762+00:00"},{"alias_kind":"pith_short_16","alias_value":"GLRPULGUK34WBEWE","created_at":"2026-07-05T11:39:06.044762+00:00"},{"alias_kind":"pith_short_8","alias_value":"GLRPULGU","created_at":"2026-07-05T11:39:06.044762+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.18564","citing_title":"Free-particle Green's function matrix elements over spherical Gaussian and plane-wave-modulated Gaussian basis functions","ref_index":47,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GLRPULGUK34WBEWEX4NHCGAXI7","json":"https://pith.science/pith/GLRPULGUK34WBEWEX4NHCGAXI7.json","graph_json":"https://pith.science/api/pith-number/GLRPULGUK34WBEWEX4NHCGAXI7/graph.json","events_json":"https://pith.science/api/pith-number/GLRPULGUK34WBEWEX4NHCGAXI7/events.json","paper":"https://pith.science/paper/GLRPULGU"},"agent_actions":{"view_html":"https://pith.science/pith/GLRPULGUK34WBEWEX4NHCGAXI7","download_json":"https://pith.science/pith/GLRPULGUK34WBEWEX4NHCGAXI7.json","view_paper":"https://pith.science/paper/GLRPULGU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.16733&json=true","fetch_graph":"https://pith.science/api/pith-number/GLRPULGUK34WBEWEX4NHCGAXI7/graph.json","fetch_events":"https://pith.science/api/pith-number/GLRPULGUK34WBEWEX4NHCGAXI7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GLRPULGUK34WBEWEX4NHCGAXI7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GLRPULGUK34WBEWEX4NHCGAXI7/action/storage_attestation","attest_author":"https://pith.science/pith/GLRPULGUK34WBEWEX4NHCGAXI7/action/author_attestation","sign_citation":"https://pith.science/pith/GLRPULGUK34WBEWEX4NHCGAXI7/action/citation_signature","submit_replication":"https://pith.science/pith/GLRPULGUK34WBEWEX4NHCGAXI7/action/replication_record"}},"created_at":"2026-07-05T11:39:06.044762+00:00","updated_at":"2026-07-05T11:39:06.044762+00:00"}