{"id":"W4417026731","doi":"10.4230/lipics.approx/random.2025.37","title":"Permanental Rank vs Determinantal Rank of Random Matrices over Finite Fields","year":2025,"lang":"en","type":"article","venue":"ArXiv.org","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University; University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Rank (graph theory); Matrix (chemical analysis); Block matrix; Random matrix; Finite field; Algebraic number; Zero (linguistics); Random element","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":[0.004970632,0.0005625493,0.0009288556,0.002050703,0.001277788,0.002770861,0.001552866,0.001339077,0.004721837],"category_scores_gemma":[0.03561124,0.0005490365,0.00068506,0.00112959,0.006991864,0.00905802,0.002348648,0.002612191,0.0004461754],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001778546,"about_ca_system_score_gemma":0.0006750266,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006272105,"about_ca_topic_score_gemma":0.0003669383,"domain_scores_codex":[0.9972968,0.001086312,0.0001069961,0.0005088529,0.000587449,0.0004136226],"domain_scores_gemma":[0.9425232,0.0453948,0.004384088,0.003758149,0.001411667,0.00252809],"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":[0.0001135751,0.00003927388,0.00185449,0.0000863138,0.00001320634,0.0001025994,0.0002420204,0.01282854,0.0008179067,0.9780115,0.001037894,0.004852668],"study_design_scores_gemma":[0.00003599167,0.00009823895,0.001292828,0.00004311009,0.00001321607,0.0002540551,0.0001101023,0.06478722,0.001093142,0.9308381,0.001397366,0.00003657199],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6487338,0.002826552,0.3069113,0.007992233,0.000202561,0.00008457404,0.0006552418,0.0004826635,0.03211116],"genre_scores_gemma":[0.9891985,0.0007652754,0.006110698,0.0002563872,0.0004541278,0.00006939228,0.0001552326,0.00007289983,0.002917516],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004970632,"threshold_uncertainty_score":0.0262875,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02062180166971331,"score_gpt":0.2947452479061064,"score_spread":0.2741234462363931,"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."}}