{"id":"W4389115365","doi":"10.48550/arxiv.2311.14863","title":"Geometric interactions between bricks and $τ$-rigidity","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Japan Society for the Promotion of Science; Natural Sciences and Engineering Research Council of Canada; Canadian Defence Academy","keywords":"Indecomposable module; Brick; Pure mathematics; Rigidity (electromagnetism); Representation (politics); Mathematics; Algebra over a field; Physics; Engineering; Quantum mechanics","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0001783405,0.0002987898,0.000459078,0.000463276,0.0001793768,0.00007396771,0.0004559428,0.000316397,0.00006439562],"category_scores_gemma":[0.0002336937,0.0003323023,0.0001953144,0.000688656,0.00009090686,0.0001201485,0.001303374,0.0007830135,0.00004734025],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000174867,"about_ca_system_score_gemma":0.00007671104,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003533652,"about_ca_topic_score_gemma":0.000046705,"domain_scores_codex":[0.9985827,0.00008204505,0.0002262469,0.0007281948,0.00009636114,0.0002844794],"domain_scores_gemma":[0.9980928,0.0007103212,0.000253847,0.0006647977,0.0001118732,0.0001663131],"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":[0.00003080131,0.00007102928,0.02330725,0.000313568,0.0005480976,0.0001210929,0.0002484849,0.001668991,0.000002261404,0.9696381,0.003480881,0.0005694203],"study_design_scores_gemma":[0.0003069958,0.0000247441,0.007351246,0.00006933929,0.000295968,0.000002308034,0.00009176617,0.001917505,0.00001735085,0.989161,0.0004212925,0.0003405293],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9698475,0.00002615592,0.02693545,0.0000594609,0.00145895,0.0002774386,0.00005120045,0.0003106531,0.001033172],"genre_scores_gemma":[0.9955716,0.0001131994,0.0001670109,0.0000118525,0.0003370258,0.00000120105,0.00002281234,0.00004415244,0.003731161],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02676843,"threshold_uncertainty_score":0.9999129,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2432284643486786,"score_gpt":0.2550608299464827,"score_spread":0.01183236559780407,"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."}}