{"id":"W4407702284","doi":"10.1137/24m164344x","title":"Everything Is Possible: Constructing Spectrahedra with Prescribed Facial Dimensions","year":2025,"lang":"en","type":"article","venue":"SIAM Journal on Optimization","topic":"Liquid Crystal Research Advancements","field":"Materials Science","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo; Kensington Health","funders":"Natural Sciences and Engineering Research Council of Canada; Australian Respiratory Council","keywords":"Mathematics; Mathematical optimization; Algebra over a field; Calculus (dental); Pure mathematics; Orthodontics","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":[0.0005567097,0.0006247039,0.0007366921,0.0005117669,0.0007229584,0.000939819,0.001247535,0.0008436901,0.005418395],"category_scores_gemma":[0.002264691,0.0004320597,0.0006589781,0.0005466414,0.001394105,0.001209916,0.002160891,0.001789214,0.001089868],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005951764,"about_ca_system_score_gemma":0.000728904,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00143468,"about_ca_topic_score_gemma":0.002691718,"domain_scores_codex":[0.9997236,0.00007830063,0.00001044853,0.0000399548,0.00009783779,0.0000497542],"domain_scores_gemma":[0.9995426,0.0002087698,0.00002904948,0.0001026848,0.00006213276,0.00005480598],"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":[0.0002155373,0.0001063797,0.0005708953,0.0001753914,0.00001954489,0.0001020206,0.0003164817,0.221106,0.006066695,0.6455578,0.007897915,0.1178653],"study_design_scores_gemma":[0.00005598365,0.0000675561,0.00007862913,0.00004882221,0.000009113585,0.00005124093,0.0001695677,0.5868565,0.002599704,0.4030519,0.006995134,0.00001580211],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1074728,0.0001854895,0.8541973,0.0005121614,0.0001474276,0.0001157781,0.0003490867,0.0005343102,0.03648572],"genre_scores_gemma":[0.3956822,0.0002218399,0.5953979,0.000210372,0.00002921337,0.0002165903,0.000342402,0.0004527196,0.007446807],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005418395,"threshold_uncertainty_score":0.01812631,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01332729680817567,"score_gpt":0.2881948608291784,"score_spread":0.2748675640210028,"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."}}