{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001428037,0.0008778688,0.0004411051,0.001968504,0.0006709634,0.0014136,0.0007646005,0.0007586813,0.007991275],"category_scores_gemma":[0.006100875,0.0003511196,0.000639897,0.0005475127,0.002185492,0.003551233,0.002288193,0.002125993,0.0009394295],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001094529,"about_ca_system_score_gemma":0.0004127369,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005628389,"about_ca_topic_score_gemma":0.000460551,"domain_scores_codex":[0.9993715,0.0001263059,0.00002534696,0.0001637459,0.0002340655,0.0000790812],"domain_scores_gemma":[0.9982503,0.0007179878,0.000232712,0.0001543683,0.0004501122,0.0001944988],"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":[0.00001672609,0.00000472907,0.0002271408,0.00004013313,0.000004340927,0.00003447161,0.00006857355,0.001644379,0.002610741,0.988425,0.000518278,0.006405408],"study_design_scores_gemma":[0.00001109292,0.00008844562,0.001068145,0.00005825634,0.00001524505,0.0003654537,0.0001778558,0.06254449,0.006048445,0.9131988,0.01638749,0.00003635219],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.08888929,0.001334683,0.8461811,0.001059309,0.0002593651,0.00004927945,0.000171689,0.0001806924,0.06187458],"genre_scores_gemma":[0.8355266,0.001594069,0.1213731,0.0004831008,0.0003407523,0.0001930549,0.0002076584,0.0002429174,0.04003869],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007991275,"threshold_uncertainty_score":0.02673352,"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."}}