{"id":"W4362725540","doi":"10.33140/jmtcm.02.02.02","title":"Hadamard Matrix Conjecture","year":2023,"lang":"en","type":"article","venue":"Journal of Mathematical Techniques and Computational Mathematics","topic":"graph theory and CDMA systems","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Saint John Regional Hospital","funders":"","keywords":"Hadamard's inequality; Hadamard matrix; Hadamard three-lines theorem; Hadamard transform; Complex Hadamard matrix; Conjecture; Hadamard's maximal determinant problem; Mathematics; Hadamard product; Hadamard three-circle theorem; Matrix (chemical analysis); Rank (graph theory); Combinatorics; Pure mathematics; Mathematical analysis; Materials science","routes":{"ca_aff":true,"ca_fund":false,"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":[0.002214311,0.0004645105,0.001029139,0.0009661369,0.002270881,0.002792431,0.0008550268,0.002434633,0.01080144],"category_scores_gemma":[0.01067094,0.0004000381,0.0007520184,0.0007752606,0.004528359,0.00557175,0.002330241,0.004303503,0.002151508],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009032841,"about_ca_system_score_gemma":0.000821571,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009278083,"about_ca_topic_score_gemma":0.0005501274,"domain_scores_codex":[0.9980477,0.0004380705,0.00009075011,0.0005519526,0.0005588588,0.0003126828],"domain_scores_gemma":[0.9943791,0.002646053,0.0003841048,0.001248912,0.0009893198,0.000352509],"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":[0.00003699465,0.00001317942,0.0002428885,0.00003982171,0.000007996194,0.00009461388,0.0001473087,0.0007221459,0.0006267085,0.9872067,0.006145455,0.00471627],"study_design_scores_gemma":[0.00002028818,0.00002276185,0.0001654423,0.00002110619,0.000004550373,0.0001683749,0.00006407218,0.003072614,0.0006503217,0.9861929,0.009602405,0.00001508731],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.2918798,0.009758457,0.2802525,0.05583317,0.004292355,0.0001088377,0.001405486,0.001033552,0.3554359],"genre_scores_gemma":[0.9270692,0.00246181,0.03243757,0.005132863,0.002603174,0.0000995981,0.0006467102,0.0001019821,0.02944696],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01080144,"threshold_uncertainty_score":0.03613442,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01092776684937778,"score_gpt":0.2547783292503364,"score_spread":0.2438505624009586,"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."}}