{"id":"W2985572810","doi":"10.4171/jncg/451","title":"Immersions and the unbounded Kasparov product: embedding spheres into Euclidean space","year":2022,"lang":"en","type":"article","venue":"Journal of Noncommutative Geometry","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University","funders":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","keywords":"Mathematics; Product (mathematics); Connection (principal bundle); Embedding; Bounded function; SPHERES; Euclidean space; Unit sphere; Space (punctuation); Pure mathematics; Unit (ring theory); Euclidean geometry; Combinatorics; Discrete mathematics; Mathematical analysis; Physics; Geometry","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":[0.0003265382,0.0004528569,0.0003339238,0.001182136,0.0009675362,0.001440607,0.0004762484,0.0004895178,0.003767563],"category_scores_gemma":[0.0009648404,0.0002131868,0.0004123952,0.0004261461,0.00201101,0.002856895,0.002163984,0.0009277425,0.0005247867],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005523509,"about_ca_system_score_gemma":0.0002941133,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008066249,"about_ca_topic_score_gemma":0.0005693183,"domain_scores_codex":[0.9996062,0.00006999236,0.00001956424,0.00007079918,0.0001323789,0.0001010784],"domain_scores_gemma":[0.9996587,0.00005541168,0.00005528083,0.00004935731,0.00005699675,0.0001243139],"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":[0.00002633875,0.00001049934,0.0003139849,0.00001744309,0.000003002014,0.0001426424,0.0004666116,0.001477467,0.003753868,0.9901578,0.0002066908,0.003423703],"study_design_scores_gemma":[0.00001110991,0.00006298709,0.0009040628,0.00001670071,0.000005892602,0.0003143252,0.0004765266,0.0226173,0.005741495,0.9642804,0.00554121,0.00002808301],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.864457,0.0001974188,0.09858012,0.000254423,0.00007765149,0.00002924703,0.00007297556,0.0002209856,0.03611016],"genre_scores_gemma":[0.9833065,0.0001017032,0.01076468,0.00004291169,0.00003833948,0.0000197283,0.00006758893,0.00008911442,0.005569561],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003767563,"threshold_uncertainty_score":0.0126037,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03071772401304518,"score_gpt":0.372055544212912,"score_spread":0.3413378201998668,"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."}}