{"id":"W3007604789","doi":"10.1017/s0305004121000256","title":"Sphere tangencies, line incidences and Lie’s line-sphere correspondence","year":2021,"lang":"en","type":"preprint","venue":"Mathematical Proceedings of the Cambridge Philosophical Society","topic":"Computational Geometry and Mesh Generation","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Isomorphism (crystallography); SPHERES; Incidence (geometry); Mathematics; Line (geometry); Combinatorics; Geometry; Physics; Crystallography","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":[0.0009742993,0.00046187,0.0007253449,0.00003513092,0.0002874196,0.0005469435,0.001891636,0.0005255043,0.0000373057],"category_scores_gemma":[0.0008755141,0.0003444518,0.0005658747,0.0007437861,0.0004506432,0.0004127835,0.004826685,0.001180136,0.000008765407],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001198129,"about_ca_system_score_gemma":0.0003640218,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008085209,"about_ca_topic_score_gemma":8.902126e-7,"domain_scores_codex":[0.9965501,0.0000410774,0.00084494,0.0009568826,0.001230485,0.000376518],"domain_scores_gemma":[0.9974235,0.0004078927,0.0005938284,0.0004720513,0.0008715249,0.0002311927],"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":[0.00004049038,0.0006745258,0.000236732,0.004685646,0.0003221494,0.000008456017,0.00253498,0.001057888,0.008317939,0.9702908,0.006564335,0.005266062],"study_design_scores_gemma":[0.0003660546,0.0001585395,0.0006478813,0.001481119,0.0001460968,0.0001204077,0.0003224738,0.2882531,0.008227121,0.6992483,0.0003066121,0.0007223109],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7927133,0.00345207,0.153845,0.04386595,0.0009870906,0.001209247,0.00004348762,0.000276297,0.003607542],"genre_scores_gemma":[0.9159564,0.0002087568,0.08157194,0.0009609554,0.000658251,0.0000584964,0.000008860623,0.00002683923,0.0005494462],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2871953,"threshold_uncertainty_score":0.9999008,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03191924192922762,"score_gpt":0.2576296744207331,"score_spread":0.2257104324915055,"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."}}