{"id":"W1726244176","doi":"","title":"Comment on \\The Hadamard circulant conjecture\"","year":2011,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"graph theory and CDMA systems","field":"Engineering","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University; University of Manitoba","funders":"","keywords":"Circulant matrix; Hadamard matrix; Conjecture; Mathematics; Hadamard transform; Combinatorics; Hadamard three-lines theorem; Hadamard's inequality; Hadamard's maximal determinant problem; Matrix (chemical analysis); Identity matrix; Complex Hadamard matrix; Permutation matrix; Physics; Eigenvalues and eigenvectors; Mathematical analysis; Quantum mechanics","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0002525051,0.0003388279,0.0003050621,0.0001253262,0.0001182793,0.00003530135,0.0006936472,0.0002778114,0.0002376452],"category_scores_gemma":[0.000008230671,0.0002949428,0.0002493456,0.0001589444,0.00008945602,0.00003506733,0.0002141316,0.000726712,0.0002953591],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000133364,"about_ca_system_score_gemma":0.00002078672,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00007254884,"about_ca_topic_score_gemma":0.00001529144,"domain_scores_codex":[0.9989147,0.0001556039,0.0001594583,0.000414102,0.0000620237,0.0002940825],"domain_scores_gemma":[0.9987267,0.0001108718,0.0000758768,0.0009499595,0.00002897984,0.0001076382],"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":[0.00003648258,0.00005164144,0.0004893526,0.0001720485,0.0004273253,0.0002082046,0.000425344,0.2130258,0.0000478841,0.7738914,0.01116529,0.00005920854],"study_design_scores_gemma":[0.002168853,0.0003166526,0.00221986,0.001563313,0.0008816572,0.00004466138,0.001646805,0.1727296,0.005489592,0.6483399,0.1606568,0.003942325],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9041727,0.0002132158,0.01640585,0.0004090012,0.003021788,0.0009058259,0.00008270524,0.0008378769,0.07395104],"genre_scores_gemma":[0.9990001,0.00008918715,0.000005373106,0.0004292835,0.00007823326,0.000002925701,0.00001714116,0.00003991359,0.0003378619],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1494915,"threshold_uncertainty_score":0.9999503,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0678257273384302,"score_gpt":0.1462636615740821,"score_spread":0.0784379342356519,"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."}}