{"id":"W7125569477","doi":"","title":"Crofton and Blaschke–Petkantschin Formulae:Applications in Stereology and Intersection Probabilities","year":2025,"lang":"","type":"dissertation","venue":"","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Intersection (aeronautics); Stereology; Field (mathematics); Dimension (graph theory); Population","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0007423823,0.0006455112,0.001043002,0.001696368,0.0003091023,0.0002285209,0.0002154924,0.0007092076,0.0002344085],"category_scores_gemma":[0.0008845334,0.0005978521,0.0001110451,0.001007994,0.000172941,0.0004529688,0.0002021934,0.0006525363,0.00000506938],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001359924,"about_ca_system_score_gemma":0.0002698114,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001070668,"about_ca_topic_score_gemma":0.008659243,"domain_scores_codex":[0.9967188,0.0001509346,0.001452152,0.0009001744,0.000246024,0.0005319511],"domain_scores_gemma":[0.9969689,0.001668429,0.0004903917,0.000421738,0.000345458,0.0001050992],"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":[0.0003913997,0.0005823332,0.006542472,0.03142814,0.0002875095,0.000002985125,0.03435167,0.000005657842,0.00007438342,0.901304,0.000162168,0.02486729],"study_design_scores_gemma":[0.002083292,0.0006330611,0.006215795,0.002064805,0.0004700625,0.00003478418,0.1656334,0.002701446,0.001760218,0.8139004,0.003187358,0.001315347],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9595154,0.002930779,0.01040414,0.0001998183,0.0003744999,0.002391824,0.00008462113,0.00008526253,0.02401368],"genre_scores_gemma":[0.926226,0.002664599,0.002666265,0.00008951137,0.00008271268,0.0008184029,0.0003886869,0.00004865091,0.06701513],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1312817,"threshold_uncertainty_score":0.9996473,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02573760607088169,"score_gpt":0.3179035868831999,"score_spread":0.2921659808123181,"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."}}