{"id":"W2108737894","doi":"10.1016/j.jcta.2009.10.007","title":"Partitions and indivisibility properties of countable dimensional vector spaces","year":2009,"lang":"en","type":"article","venue":"Journal of Combinatorial Theory Series A","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Calgary","funders":"","keywords":"Countable set; Counterexample; Partition (number theory); Vector space; Affine transformation; Mathematics; Space (punctuation); Pure mathematics; Discrete mathematics; Computer science; Combinatorics","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":[],"consensus_categories":[],"category_scores_codex":[0.001203363,0.0001142952,0.0003896932,0.0000601889,0.0001267556,0.00001586676,0.0001171966,0.00008492987,0.00007800859],"category_scores_gemma":[0.0009340129,0.00008258499,0.00007780924,0.00007817166,0.0004141337,0.0003952574,0.00003061672,0.0002100666,6.503709e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002397748,"about_ca_system_score_gemma":0.00008241329,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":6.084671e-7,"about_ca_topic_score_gemma":7.043238e-7,"domain_scores_codex":[0.998877,0.0002478281,0.0004456264,0.00008470866,0.0002049118,0.0001399339],"domain_scores_gemma":[0.9987451,0.0003741492,0.0004195309,0.0001451934,0.0002506246,0.00006544642],"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":[0.001635299,0.0002647541,0.0001385471,0.0000352411,0.00005966017,0.000006827343,0.0008507044,0.000006779115,0.005225317,0.9914573,0.000202982,0.0001166093],"study_design_scores_gemma":[0.0007450852,0.0008183082,0.0003825093,0.00009503929,0.00005565205,0.00008461175,0.000576022,0.000001180527,0.02010424,0.9765663,0.0004869198,0.00008412668],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9972042,0.0007143829,0.0001501271,0.0004426685,0.0008952569,0.00009784957,0.000006100375,0.00001257447,0.0004768428],"genre_scores_gemma":[0.9986688,0.00004021029,0.000945923,0.00004138239,0.0001597855,0.000001109489,3.588097e-7,0.00000676123,0.000135594],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01489097,"threshold_uncertainty_score":0.3367718,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02486086334413082,"score_gpt":0.2822014688557475,"score_spread":0.2573406055116166,"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."}}