{"id":"W3024316797","doi":"10.37236/9617","title":"Zero-Sum Squares in Bounded Discrepancy $\\{-1,1\\}$-Matrices","year":2021,"lang":"en","type":"preprint","venue":"The Electronic Journal of Combinatorics","topic":"Mathematical Approximation and Integration","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Banff International Research Station for Mathematical Innovation and Discovery","keywords":"Zero (linguistics); Square matrix; Diagonal; Mathematics; Combinatorics; Matrix (chemical analysis); Square (algebra); Diagonal matrix; Bounded function; Main diagonal; Symmetric matrix; Physics; Mathematical analysis; Eigenvalues and eigenvectors; Geometry; Quantum mechanics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["research_integrity"],"consensus_categories":[],"category_scores_codex":[0.002590434,0.0003614481,0.0009039425,0.0002623484,0.00009981665,0.0002739704,0.0009515836,0.0003003653,0.00008503839],"category_scores_gemma":[0.001587089,0.0002339035,0.0004198741,0.0004901119,0.00006915439,0.000214977,0.0002774494,0.002747966,0.000005374113],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007453387,"about_ca_system_score_gemma":0.001142109,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001422235,"about_ca_topic_score_gemma":0.00006266041,"domain_scores_codex":[0.9964791,0.0004619361,0.001344486,0.0002289625,0.0009164874,0.0005690604],"domain_scores_gemma":[0.9962581,0.0008670332,0.001620597,0.0006121282,0.0005574183,0.0000846889],"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":[0.00003254251,0.0004804045,0.0000368818,0.0003958241,0.0001294618,0.0000121257,0.001306702,0.00001060279,0.0000246477,0.9963061,0.0009563649,0.0003083378],"study_design_scores_gemma":[0.0006038144,0.0001801604,0.00003096649,0.0006488033,0.0001555164,0.00009060247,0.0006453599,0.001157734,0.000735568,0.9948504,0.0006645116,0.0002365481],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7919586,0.0102056,0.1862409,0.004240547,0.00133521,0.0008180372,0.00000375994,0.00006383442,0.005133439],"genre_scores_gemma":[0.9959881,0.001811006,0.001420694,0.00005390246,0.0001237909,0.00002306897,0.000007854793,0.00004764881,0.0005239857],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2040294,"threshold_uncertainty_score":0.9995527,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02904234464443128,"score_gpt":0.3156276403240214,"score_spread":0.2865852956795901,"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."}}