{"id":"W4384918760","doi":"10.48550/arxiv.2307.09663","title":"Spectral Applications of Vertex-Clique Incidence Matrices Associated with a Graph","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Graph theory and applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Combinatorics; Mathematics; Clique graph; Block graph; Discrete mathematics; Split graph; Line graph; Simplex graph; Vertex (graph theory); Spectral graph theory; Graph power; Graph; Pathwidth","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":[0.0003522546,0.0002655121,0.0004052435,0.0003558994,0.0001572937,0.00002275308,0.0008015626,0.0002433227,0.00003434866],"category_scores_gemma":[0.0001073047,0.000279014,0.0002119595,0.001625278,0.0002526507,0.00009014142,0.0003426985,0.0004819818,0.00004189073],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009183625,"about_ca_system_score_gemma":0.0001393331,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001112387,"about_ca_topic_score_gemma":0.0005191887,"domain_scores_codex":[0.9986205,0.00011995,0.000274053,0.0006212228,0.0001056951,0.0002586488],"domain_scores_gemma":[0.9974407,0.0007427373,0.0005742263,0.0009148181,0.0002251602,0.0001023575],"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":[0.00003438547,0.0002444181,0.006008343,0.0001844811,0.0002686061,0.00002521093,0.0001629732,0.003596089,0.00005091777,0.989139,0.0002678374,0.0000176908],"study_design_scores_gemma":[0.0002592967,0.00003935637,0.004020479,0.0002165581,0.0003810402,0.000001760208,0.0002039455,0.001508503,0.0002667399,0.992772,0.00002554829,0.0003047842],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9433686,0.00001971736,0.05352945,0.00005305045,0.00004223803,0.0008998049,0.0001882479,0.0003904878,0.001508379],"genre_scores_gemma":[0.9975534,0.0001428837,0.0007551709,0.00001123981,0.00001742451,0.00002682769,0.00005921139,0.00004135598,0.001392483],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05418478,"threshold_uncertainty_score":0.9999662,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08955239206976333,"score_gpt":0.2276439287051913,"score_spread":0.1380915366354279,"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."}}