{"id":"W2981227476","doi":"10.3934/dcds.2020052","title":"Type Ⅱ finite time blow-up for the energy critical heat equation in <inline-formula><tex-math id=\"M1\">$ \\mathbb{R}^4 $</tex-math></inline-formula>","year":2019,"lang":"en","type":"article","venue":"Discrete and Continuous Dynamical Systems","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":25,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"Engineering and Physical Sciences Research Council","keywords":"Energy (signal processing); Physics; Type (biology); Combinatorics; Heat equation; Mathematical physics; Mathematics; Quantum mechanics","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.001592934,0.001152714,0.002193846,0.0002288195,0.000406327,0.0004533626,0.0009427716,0.0007294574,0.00006451377],"category_scores_gemma":[0.001796388,0.0008401548,0.0005380948,0.000631528,0.000378157,0.0007415149,0.0004654901,0.0006532516,0.0002644659],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003085425,"about_ca_system_score_gemma":0.0001447583,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00006799294,"about_ca_topic_score_gemma":0.0000995523,"domain_scores_codex":[0.9930359,0.0003077829,0.002386064,0.001335863,0.001264848,0.001669542],"domain_scores_gemma":[0.9911447,0.005648606,0.0005518312,0.001555807,0.0006224801,0.0004766416],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0002953337,0.0004743006,0.0000384991,0.001513446,0.0002377388,0.00002067257,0.000650843,0.0008279908,0.01626883,0.9769681,0.0004622267,0.002242032],"study_design_scores_gemma":[0.002362778,0.0005970579,0.00002939616,0.0009637063,0.0003128404,0.00005094495,0.0001974747,0.8335253,0.0001694855,0.1542863,0.006424403,0.001080303],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6521977,0.003436378,0.3264118,0.001460652,0.002300677,0.00713623,0.0008626134,0.0008994048,0.005294497],"genre_scores_gemma":[0.9886382,0.0001365602,0.003722598,0.0002443758,0.000570655,0.0006237259,0.0004549298,0.0003069839,0.005301929],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.8326973,"threshold_uncertainty_score":0.9994049,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01745763299337103,"score_gpt":0.2750456482443566,"score_spread":0.2575880152509855,"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."}}