{"id":"W6966628651","doi":"10.48550/arxiv.0707.4201","title":"Noncommutative geometry and lower dimensional volumes in Riemannian geometry","year":2007,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Noncommutative and Quantum Gravity Theories","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Noncommutative geometry; Riemannian geometry; Manifold (fluid mechanics); Riemannian manifold; Spectral triple; Noncommutative algebraic geometry; Dirac (video compression format); Spectral geometry; Differential geometry","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":[0.0009672813,0.0006213082,0.0005311749,0.001613677,0.0009684976,0.002979764,0.0008518951,0.0008297745,0.00335618],"category_scores_gemma":[0.001859525,0.0002443921,0.00061038,0.00101706,0.005539904,0.006118601,0.002155627,0.002096532,0.000511587],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008850115,"about_ca_system_score_gemma":0.0003019129,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004193875,"about_ca_topic_score_gemma":0.0003842749,"domain_scores_codex":[0.9991955,0.0002559565,0.00003855372,0.0001637241,0.0002595252,0.0000867113],"domain_scores_gemma":[0.9989563,0.0004424858,0.0001740433,0.0001509408,0.0001411545,0.0001350155],"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":[0.000001805627,0.000002781341,0.00006137201,0.00001126835,0.000001700034,0.00001460199,0.0001202242,0.0002983465,0.00025478,0.9977275,0.000244075,0.001261581],"study_design_scores_gemma":[0.000001649671,0.000007938539,0.000347823,0.0000060913,0.000001869208,0.00005912367,0.00006159269,0.001420733,0.0002615459,0.9920031,0.005821585,0.000007008817],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3889052,0.02090082,0.409113,0.008169002,0.001565452,0.00004748188,0.0003268855,0.0003193639,0.1706527],"genre_scores_gemma":[0.9563304,0.003082061,0.02634372,0.0005690652,0.001088319,0.00006248566,0.0001429175,0.0001284394,0.01225266],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.00335618,"threshold_uncertainty_score":0.01122755,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03420463757247806,"score_gpt":0.2168415248094274,"score_spread":0.1826368872369493,"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."}}