{"id":"W4394780715","doi":"10.48550/arxiv.2404.07321","title":"Density of growth-rates of subgroups of a free group and the non-backtracking spectrum of the configuration model","year":2024,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Operator Algebra Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"Natural Sciences and Engineering Research Council of Canada; Hellenic Foundation for Research and Innovation; European Commission","keywords":"Backtracking; Rank (graph theory); Eigenvalues and eigenvectors; Group (periodic table); Mathematics; Spectrum (functional analysis); Set (abstract data type); Combinatorics; Matrix (chemical analysis); Computer science; Mathematical optimization; Physics; Chemistry; Quantum mechanics","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006638821,0.0002244846,0.0006332819,0.0001685895,0.00006257667,0.00001288079,0.0008632662,0.00020277,0.00001243249],"category_scores_gemma":[0.0003833684,0.0001606427,0.0002622052,0.0004568252,0.0009595798,0.0000890597,0.00172654,0.0006151947,6.687121e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006888031,"about_ca_system_score_gemma":0.0001729152,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003645552,"about_ca_topic_score_gemma":0.0004708332,"domain_scores_codex":[0.9985575,0.0001936464,0.0004499899,0.0003990161,0.000218419,0.0001813956],"domain_scores_gemma":[0.9972391,0.0006955922,0.0006139036,0.001041526,0.0003691849,0.00004065711],"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":[0.0003682187,0.0001260403,0.005037128,0.002662573,0.0002956207,0.000008153187,0.001415845,0.01285571,0.01100839,0.966176,0.00003022724,0.00001614558],"study_design_scores_gemma":[0.000755149,0.00003268187,0.001067055,0.0004001482,0.0002305621,0.000001317733,0.0003826123,0.1561426,0.1049011,0.7359709,1.394517e-7,0.0001157502],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9513404,0.00008067131,0.0468948,0.00008811952,0.00006978315,0.0006706169,0.00007798238,0.00001346876,0.0007641122],"genre_scores_gemma":[0.9989153,0.0001595429,0.0006974245,0.00000430883,0.00001593505,0.000001123062,0.000003117497,0.00002646348,0.0001767598],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2302051,"threshold_uncertainty_score":0.655082,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07556318812047982,"score_gpt":0.2405888572358847,"score_spread":0.1650256691154049,"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."}}