{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001699171,0.0004673131,0.0007015447,0.0008456756,0.001106249,0.00240792,0.0009715581,0.001441976,0.004507117],"category_scores_gemma":[0.002515855,0.000400773,0.0006001007,0.0008246448,0.004075888,0.003182034,0.001814299,0.001807103,0.0006371757],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000961385,"about_ca_system_score_gemma":0.00115366,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001531537,"about_ca_topic_score_gemma":0.0008091308,"domain_scores_codex":[0.9992144,0.0003166312,0.00003742953,0.00007901887,0.0002721056,0.00008042867],"domain_scores_gemma":[0.9992502,0.000228728,0.0000772411,0.0001500181,0.0001574114,0.0001364199],"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":[0.00001184809,0.000006100642,0.00002926167,0.00001050482,0.000002731766,0.00002763478,0.00005776647,0.00212311,0.0004118256,0.9945047,0.0004166554,0.002397934],"study_design_scores_gemma":[0.00001114035,0.00001665657,0.00004493387,0.00001018172,0.000002102681,0.00004799452,0.00004016833,0.03544024,0.000820504,0.9607602,0.00278977,0.00001605433],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.09059137,0.0008630009,0.8583615,0.00227421,0.0005047348,0.0001222048,0.0001616154,0.0002982998,0.0468231],"genre_scores_gemma":[0.7111139,0.0008654601,0.2741375,0.00061938,0.0002778171,0.0002541735,0.0001422331,0.0002708677,0.01231864],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004507117,"threshold_uncertainty_score":0.01507783,"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."}}