{"id":"W4408655672","doi":"10.61091/jcmcc124-49","title":"A decomposition into boxes that determine the Kernel of a staircase starshaped set in \\(\\mathbb{R}^d\\)","year":2025,"lang":"en","type":"article","venue":"Journal of Combinatorial Mathematics and Combinatorial Computing","topic":"advanced mathematical theories","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Kernel (algebra); Decomposition; Set (abstract data type); Mathematics; Discrete mathematics; Combinatorics; Computer science; Chemistry; Programming language","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"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":[0.0001403504,0.0003049294,0.0003831592,0.0006688872,0.0006818167,0.001622276,0.0006545057,0.0004526022,0.005738468],"category_scores_gemma":[0.0005721925,0.0004025744,0.0005514149,0.0004310133,0.0008190844,0.001197261,0.0009464636,0.0007813888,0.00111039],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006237187,"about_ca_system_score_gemma":0.0006537953,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004641467,"about_ca_topic_score_gemma":0.003448347,"domain_scores_codex":[0.9997626,0.00001420008,0.00001166987,0.0000597216,0.00006583814,0.00008597384],"domain_scores_gemma":[0.9995441,0.00008954079,0.00006474882,0.00006585339,0.0001257907,0.0001099649],"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":[0.0006532076,0.0002468204,0.01123615,0.0002496838,0.00005632083,0.0009743053,0.001931897,0.01282364,0.09741323,0.8168854,0.005031552,0.05249774],"study_design_scores_gemma":[0.0002100255,0.0003698842,0.02801236,0.0003284661,0.0001442213,0.00291751,0.003308067,0.2389702,0.09080268,0.5838003,0.05095434,0.0001818816],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7387245,0.0002091796,0.2360626,0.0001003697,0.0000379567,0.00009977036,0.0007429379,0.0003680562,0.02365462],"genre_scores_gemma":[0.857914,0.0001995164,0.1251014,0.00005895883,0.00002118544,0.0001317148,0.001714361,0.0001995372,0.01465936],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005738468,"threshold_uncertainty_score":0.01919711,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02570656957595447,"score_gpt":0.3341019136807096,"score_spread":0.3083953441047552,"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."}}