{"id":"W4379086819","doi":"10.48550/arxiv.2305.19320","title":"On the algebraic proof complexity of Tensor Isomorphism","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Parallel Computing and Optimization Techniques","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Mathematics; Isomorphism (crystallography); Rank (graph theory); Linear algebra; Upper and lower bounds; Combinatorics; Algebraic number; Tensor (intrinsic definition); Bounded function; Conjecture; Discrete mathematics; Algebra over a field; Pure mathematics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.009118901,0.00128304,0.001963368,0.002135851,0.003049399,0.006913876,0.004424842,0.002155551,0.01634904],"category_scores_gemma":[0.06539991,0.00140541,0.002842238,0.00337953,0.007174745,0.02819103,0.008694859,0.0109497,0.002159442],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.005802441,"about_ca_system_score_gemma":0.004357837,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004494937,"about_ca_topic_score_gemma":0.004566493,"domain_scores_codex":[0.9850455,0.005283022,0.0007974809,0.002391674,0.004690682,0.001791676],"domain_scores_gemma":[0.8595917,0.122738,0.003626231,0.008445024,0.003696109,0.001902921],"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":[0.0003635218,0.0002171928,0.002186969,0.0007425335,0.0001251383,0.0002324251,0.0008435543,0.03492187,0.00212921,0.8852304,0.01561858,0.0573885],"study_design_scores_gemma":[0.00005362745,0.00002868481,0.0003992834,0.00005429919,0.00004629668,0.00008608296,0.0001055281,0.07258838,0.0009250533,0.9206986,0.00498538,0.00002877578],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1420188,0.006054942,0.7138672,0.04789348,0.0007372814,0.0004005476,0.002157365,0.002796203,0.08407421],"genre_scores_gemma":[0.7053786,0.004684556,0.2618353,0.004311055,0.002159272,0.0006510139,0.002839818,0.001483578,0.01665678],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01634904,"threshold_uncertainty_score":0.05469298,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1728259515000753,"score_gpt":0.2151925318202324,"score_spread":0.04236658032015714,"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."}}