{"id":"W2160377742","doi":"10.1007/s00205-011-0464-5","title":"Unique Solutions to Hartree–Fock Equations for Closed Shell Atoms","year":2011,"lang":"en","type":"article","venue":"Archive for Rational Mechanics and Analysis","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":16,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"Studienstiftung des Deutschen Volkes; University of Toronto","keywords":"Hartree–Fock method; Open shell; Complex system; Mathematical physics; Shell (structure); Physics; Statistical physics; Mathematics; Quantum mechanics; Materials science; Computer science; Artificial intelligence","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0016237,0.001198448,0.001248846,0.001873179,0.002368822,0.003371863,0.00244083,0.002888868,0.007225666],"category_scores_gemma":[0.006378038,0.0008739113,0.001250976,0.001343015,0.004858927,0.004957129,0.003520908,0.004259844,0.001000119],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001633639,"about_ca_system_score_gemma":0.002106254,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001471241,"about_ca_topic_score_gemma":0.002136851,"domain_scores_codex":[0.9992222,0.0002454393,0.00005649261,0.00009584748,0.0002530305,0.0001270897],"domain_scores_gemma":[0.9987057,0.0005023876,0.0001649444,0.0001575778,0.000276201,0.0001931318],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000007731599,0.00001088089,0.00004791706,0.00002323854,0.000004760262,0.00003202301,0.0001117284,0.001562067,0.0002860897,0.9952205,0.001038194,0.001654805],"study_design_scores_gemma":[0.00001044313,0.000004101436,0.00004923008,0.000008549743,0.000001972295,0.00003849702,0.00005634323,0.0106541,0.0001044345,0.9884663,0.0005961725,0.000009791349],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3756844,0.002519175,0.4902997,0.008914237,0.00147209,0.0001633438,0.0007839079,0.0004505702,0.1197126],"genre_scores_gemma":[0.8493902,0.001494265,0.09584975,0.001227446,0.001004261,0.0002551286,0.0007202753,0.0004168116,0.04964184],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007225666,"threshold_uncertainty_score":0.02417225,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1061123895305013,"score_gpt":0.3235082985923891,"score_spread":0.2173959090618878,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}