{"id":"W4388717843","doi":"10.48550/arxiv.2311.07727","title":"Spherical complexes","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Contractible space; Betti number; Mathematics; Homotopy; Combinatorics; Conjecture; Simplicial complex; Discrete mathematics; Ternary operation; Graph; Pure mathematics; Computer science","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":[0.0001378723,0.0002460164,0.0003471312,0.0000962449,0.0001576401,0.00004003827,0.0006972683,0.0001909868,0.0003297927],"category_scores_gemma":[0.0001094096,0.0002770319,0.00021371,0.0004134863,0.0001525113,0.00005631093,0.00124918,0.0005176179,0.000670943],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001224816,"about_ca_system_score_gemma":0.0000815045,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001108044,"about_ca_topic_score_gemma":0.0001327835,"domain_scores_codex":[0.998796,0.00009853449,0.0001932643,0.0005951854,0.00006834171,0.0002486901],"domain_scores_gemma":[0.9980827,0.0005698647,0.0001794829,0.000936919,0.0001145652,0.0001164969],"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":[0.00001557563,0.0001300469,0.001319943,0.0001154464,0.0001476322,0.00006819944,0.0002305114,0.002478751,0.00005372893,0.979884,0.01544358,0.000112546],"study_design_scores_gemma":[0.0002139306,0.00001967554,0.002072866,0.00005332086,0.0001349091,0.000001400153,0.0002496902,0.01286262,0.00006735947,0.9817164,0.002282977,0.0003248792],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7115912,0.00002558372,0.2759164,0.0004175163,0.0002577698,0.0005879275,0.0001132429,0.0008758768,0.01021448],"genre_scores_gemma":[0.9876507,0.00006365434,0.002527339,0.00004280044,0.00008539473,0.000003642292,0.0000433626,0.00005135841,0.00953173],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2760595,"threshold_uncertainty_score":0.9999682,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2869617736831569,"score_gpt":0.2691268855663412,"score_spread":0.01783488811681566,"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."}}