{"id":"W4414888100","doi":"10.48550/arxiv.2507.13121","title":"Schauder Basis with Finite Blaschke Products","year":2025,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Engineering and Materials Science Studies","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Winnipeg; Université Laval","funders":"","keywords":"Schauder basis; Holomorphic function; Hardy space; Blaschke product; Space (punctuation); Basis (linear algebra); Bergman space; Class (philosophy)","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":[0.0008491935,0.0005982016,0.0004134511,0.001690575,0.0008501893,0.001674948,0.0007737303,0.0005758124,0.004280476],"category_scores_gemma":[0.001546824,0.0002583419,0.0004876607,0.000542292,0.001774793,0.00255236,0.001921741,0.001809232,0.00142361],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007721349,"about_ca_system_score_gemma":0.000634892,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000663459,"about_ca_topic_score_gemma":0.0006817637,"domain_scores_codex":[0.9993813,0.0001222163,0.0000232029,0.000106523,0.0002459236,0.0001207617],"domain_scores_gemma":[0.999334,0.0001153103,0.00006998739,0.00007875312,0.0001867977,0.0002151149],"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":[0.00001547262,0.00001095743,0.0001048553,0.00001682983,0.000002799055,0.00002912799,0.00008245807,0.001144647,0.001882771,0.9930866,0.0003403244,0.00328302],"study_design_scores_gemma":[0.00001282249,0.00005909966,0.0003273586,0.00002559217,0.000005585226,0.000135377,0.0001466399,0.02757507,0.003843564,0.9614788,0.006359169,0.00003091911],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4605817,0.0009318142,0.4566846,0.0008590167,0.0002972541,0.0000498903,0.0002793312,0.0003120298,0.08000428],"genre_scores_gemma":[0.9109525,0.0005397814,0.05996896,0.00025163,0.0002030241,0.00009434629,0.0003312678,0.0001754347,0.02748304],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004280476,"threshold_uncertainty_score":0.0143196,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02044803929010481,"score_gpt":0.2147816828211735,"score_spread":0.1943336435310687,"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."}}