{"id":"W4416026380","doi":"10.48550/arxiv.2511.04482","title":"Pivotal Brauer-Picard groupoids and graded extensions","year":2025,"lang":"","type":"preprint","venue":"ArXiv.org","topic":"Homotopy and Cohomology in Algebraic Topology","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Engineering and Physical Sciences Research Council; Natural Sciences and Engineering Research Council of Canada; American Institute of Mathematics; Norges Forskningsråd; Deutsche Forschungsgemeinschaft; Division of Mathematical Sciences; National Science Foundation","keywords":"Extension (predicate logic); Tensor (intrinsic definition); Algebra over a field; Tensor product; Statement (logic); Natural (archaeology); Tensor product of Hilbert spaces","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":[0.0007030469,0.0004844467,0.0003006677,0.001408504,0.001066954,0.002602884,0.0006111818,0.0005231453,0.00479017],"category_scores_gemma":[0.001075138,0.0002377171,0.0004590864,0.0006224239,0.002792683,0.005331126,0.002664482,0.001221532,0.0006882141],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009436085,"about_ca_system_score_gemma":0.0004503729,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00110218,"about_ca_topic_score_gemma":0.001191754,"domain_scores_codex":[0.9995385,0.00007468454,0.0000289851,0.0001076818,0.0001292384,0.0001208359],"domain_scores_gemma":[0.9993225,0.0001008292,0.0001112775,0.00009874425,0.0001222551,0.0002443946],"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":[0.0000077156,0.000005895672,0.0003722141,0.00001219464,0.000001795469,0.000056057,0.0002832729,0.0001592313,0.000863939,0.996035,0.0001852935,0.00201735],"study_design_scores_gemma":[0.000009612709,0.00005043376,0.001675245,0.00003004188,0.00001480585,0.0003255802,0.0006897009,0.00293761,0.00196092,0.9748863,0.01739595,0.00002378776],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.655729,0.001358761,0.1968284,0.001375391,0.0003488735,0.000101146,0.000312069,0.0003006717,0.1436457],"genre_scores_gemma":[0.9737776,0.0003636525,0.0106708,0.0001186326,0.0001139184,0.00003195533,0.0001379492,0.00003160018,0.01475393],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00479017,"threshold_uncertainty_score":0.01602465,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05937464270642458,"score_gpt":0.3205734597437291,"score_spread":0.2611988170373045,"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."}}