{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009256516,0.0009594996,0.0006501591,0.001224656,0.001129849,0.001383524,0.001105778,0.001440123,0.01352051],"category_scores_gemma":[0.005567089,0.000360044,0.001227742,0.0003235873,0.00191621,0.001876828,0.002161406,0.001995675,0.0007613044],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001940711,"about_ca_system_score_gemma":0.001487881,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00562556,"about_ca_topic_score_gemma":0.004412794,"domain_scores_codex":[0.9997365,0.00005849585,0.00001532464,0.00005062461,0.00007784789,0.00006122355],"domain_scores_gemma":[0.9986697,0.0006241869,0.0002076154,0.00006718076,0.0001659106,0.0002653581],"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":[0.0005384103,0.0001473421,0.004291292,0.001056269,0.0001518474,0.001966662,0.0006064491,0.1344888,0.01967449,0.8045641,0.01419037,0.01832405],"study_design_scores_gemma":[0.00006044376,0.00006473745,0.001902743,0.0001581088,0.00004155753,0.0002522144,0.0001775357,0.8004919,0.003836903,0.1894204,0.003528636,0.00006481047],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5923418,0.003775167,0.255062,0.006981615,0.00151096,0.0003375929,0.001104768,0.001529753,0.1373563],"genre_scores_gemma":[0.895709,0.000995025,0.041884,0.0007088726,0.0003018002,0.0004029727,0.001417333,0.001004999,0.05757603],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01352051,"threshold_uncertainty_score":0.04523063,"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."}}