{"id":"W4200076981","doi":"10.1002/qua.26838","title":"Two projector triple products in quantum crystallography","year":2021,"lang":"en","type":"article","venue":"International Journal of Quantum Chemistry","topic":"Crystallography and molecular interactions","field":"Chemistry","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"Saint Mary's University; Mount Saint Vincent University; Université Laval; Dalhousie University","funders":"U.S. Naval Research Laboratory; Natural Sciences and Engineering Research Council of Canada; Canada Foundation for Innovation; Mount Saint Vincent University","keywords":"Orthonormal basis; Projector; Quantum; Basis (linear algebra); Density matrix; Matrix (chemical analysis); Kernel (algebra); Scattering; Diffraction; Pure mathematics; Product (mathematics); Orthonormality; Physics; Crystallography; Mathematics; Quantum mechanics; Chemistry; Optics; Geometry","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0002092824,0.0002131597,0.0002963321,0.0001927174,0.00003988072,0.0001109708,0.0005555482,0.0001174101,0.001127896],"category_scores_gemma":[0.0005665958,0.0002177313,0.0004009786,0.0003764144,0.00008387693,0.0002424094,0.00009509647,0.0006532304,0.000002850774],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001414439,"about_ca_system_score_gemma":0.0004501145,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003535166,"about_ca_topic_score_gemma":0.00001225617,"domain_scores_codex":[0.9979292,0.00002981212,0.0008095177,0.0003071499,0.0006629123,0.0002613866],"domain_scores_gemma":[0.9978691,0.00008439264,0.000503452,0.0002761734,0.001152662,0.0001141844],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"bench_or_experimental","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.0002240144,0.0006499085,0.00204972,0.00009310496,0.000332357,0.001856703,0.0001616928,0.0001473993,0.9925464,0.0004163557,0.001140496,0.0003818231],"study_design_scores_gemma":[0.002681244,0.00002513149,0.0003307501,0.000476674,0.0000572279,0.003441372,0.001383042,0.0007192323,0.9294823,0.001469746,0.05958383,0.0003494746],"study_design_candidate":"bench_or_experimental","study_design_consensus":"bench_or_experimental","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9879305,0.001087602,0.0004055322,0.001284635,0.001104589,0.00003713946,0.0000702019,0.0000299545,0.00804979],"genre_scores_gemma":[0.9978926,0.000167129,0.0005059484,0.00009948765,0.0007232437,0.000008836833,0.00007658673,0.00002726418,0.0004989515],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.06306415,"threshold_uncertainty_score":0.9997852,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01708496458456621,"score_gpt":0.2865397157356429,"score_spread":0.2694547511510767,"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."}}