{"id":"W7108448399","doi":"10.1016/j.dam.2025.10.062","title":"<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\" id=\"d1e22\" altimg=\"si21.svg\"> <mml:mrow> <mml:mi>H</mml:mi> <mml:mi>V</mml:mi> </mml:mrow> </mml:math> -symmetric polyhedra and bipolarity","year":2025,"lang":"en","type":"article","venue":"Discrete Applied Mathematics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University","funders":"Japan Society for the Promotion of Science; Japan Society for the Promotion of Science London","keywords":"Polyhedron; Polytope; Vertex (graph theory); Convex polytope; Enumeration; Regular polygon; Convex hull","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0004809361,0.0006890183,0.0006977169,0.001537555,0.0007798954,0.004372079,0.001490347,0.0007326217,0.484598],"category_scores_gemma":[0.001906479,0.0005274641,0.0006845953,0.002863768,0.0005674252,0.003775248,0.00116972,0.001626719,0.26888],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001584184,"about_ca_system_score_gemma":0.0008381123,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.005218927,"about_ca_topic_score_gemma":0.008211406,"domain_scores_codex":[0.9996847,0.00006169135,0.0000265372,0.00005453154,0.0001422841,0.00003028279],"domain_scores_gemma":[0.9990589,0.0002690055,0.00006444591,0.000175207,0.0003313516,0.0001011273],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"not_applicable","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00004445961,0.00002240414,0.0001040391,0.0001718582,0.000005873055,0.00003657608,0.0001001882,0.0003236874,0.001079324,0.1183656,0.8415529,0.03819312],"study_design_scores_gemma":[0.00002398126,0.00001001466,0.0004209579,0.00004681745,0.000004252933,0.00010211,0.00007329186,0.001712551,0.001933985,0.06282048,0.9328291,0.00002234308],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.001803488,0.0004215541,0.09275758,0.005194027,0.001152392,0.0001375391,0.04987189,0.01832728,0.8303342],"genre_scores_gemma":[0.0491011,0.002297011,0.09877276,0.002291346,0.001093452,0.0004031657,0.09529335,0.03198637,0.7187614],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.484598,"threshold_uncertainty_score":0.7351584,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01923873287089201,"score_gpt":0.2670158124523098,"score_spread":0.2477770795814178,"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."}}