{"id":"W3016356691","doi":"10.2140/apde.2023.16.1651","title":"Directional square functions","year":2023,"lang":"en","type":"article","venue":"Analysis & PDE","topic":"Advanced Harmonic Analysis Research","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"Agencia Estatal de Investigación; National Science Foundation; Ministerio de Economía y Competitividad; Simons Foundation; Basque Center for Applied Mathematics; Eusko Jaurlaritza","keywords":"Mathematics; Embedding; Counterexample; Conical surface; Logarithm; Multiplier (economics); Square (algebra); Function (biology); Square root; Fourier transform; Mathematical analysis; Combinatorics; Geometry; Computer science","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":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0004935866,0.000138572,0.0003622683,0.001076543,0.000295009,0.00004199912,0.0002081232,0.000065667,0.003340523],"category_scores_gemma":[0.0005355553,0.0001255357,0.0005988438,0.008511822,0.00005851538,0.0001204427,0.0001037495,0.0002019554,0.002438114],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009993863,"about_ca_system_score_gemma":0.00004589849,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00006080867,"about_ca_topic_score_gemma":0.0005404154,"domain_scores_codex":[0.9981799,0.0001016656,0.0003178259,0.0003700323,0.0006507557,0.0003798305],"domain_scores_gemma":[0.9984382,0.0005993454,0.00008926991,0.0005548897,0.0001973351,0.0001209588],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0001221607,0.001074977,0.2860492,0.0001643859,0.04527457,0.0002475359,0.001853279,0.04882105,0.004055606,0.1054911,0.4813008,0.02554535],"study_design_scores_gemma":[0.001443042,0.000136063,0.1425368,0.00004221487,0.01888166,0.00001423282,0.005705588,0.2302028,0.001863175,0.3934191,0.2039967,0.001758622],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3307673,0.0003556609,0.6069726,0.003912493,0.0002482996,0.0004598795,0.0001363127,0.002238675,0.05490874],"genre_scores_gemma":[0.9234984,0.00008598223,0.002868022,0.00004943461,0.0001488654,0.00007877289,0.0002031432,0.00003097514,0.07303644],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6041046,"threshold_uncertainty_score":0.9983386,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1082940408145884,"score_gpt":0.4245559350012089,"score_spread":0.3162618941866205,"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."}}