{"id":"W2963794320","doi":"10.23638/lmcs-15(3:3)2019","title":"Subspace-Invariant AC$^0$ Formulas","year":2019,"lang":"en","type":"article","venue":"DOAJ (DOAJ: Directory of Open Access Journals)","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Invariant (physics); Mathematics; Invariant subspace problem; Subspace topology; Pure mathematics; Invariant subspace; Mathematical analysis; Mathematical physics; Linear subspace; Banach space","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","scholarly_communication","open_science","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00226742,0.0003724725,0.0007779778,0.0006809582,0.0002630202,0.002641198,0.008513358,0.0001347026,0.009117214],"category_scores_gemma":[0.0001472945,0.0003177939,0.0002736653,0.001398998,0.00007847271,0.006142365,0.002702447,0.0004741602,0.0003561328],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007830852,"about_ca_system_score_gemma":0.000203823,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001951469,"about_ca_topic_score_gemma":0.00001112501,"domain_scores_codex":[0.9967229,0.000328984,0.0007872421,0.0006766477,0.0008688906,0.0006152882],"domain_scores_gemma":[0.9968327,0.0004424544,0.0007719615,0.001316921,0.000270852,0.0003650874],"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":[0.0006395812,0.001541661,0.2370542,0.0006197411,0.0009653903,0.0005863249,0.002263946,0.001834551,0.226259,0.2564324,0.1091914,0.1626118],"study_design_scores_gemma":[0.003852346,0.0001407865,0.2843026,0.00132032,0.0001435372,0.000301114,0.0001960988,0.02420543,0.1795838,0.3686846,0.1341553,0.003114091],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7821758,0.0123426,0.1332892,0.001386541,0.00511433,0.001742415,0.00004512411,0.0003383828,0.06356557],"genre_scores_gemma":[0.9882935,0.001959373,0.005346385,0.0006853768,0.000276682,0.00002584183,0.000004449147,0.00004918251,0.00335924],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2061176,"threshold_uncertainty_score":0.9999274,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.151290589325699,"score_gpt":0.5019648049511604,"score_spread":0.3506742156254613,"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."}}