{"id":"W4403815834","doi":"10.48550/arxiv.2409.20455","title":"Planarity of compactifications of $\\mathbb{R}$ with arc-like remainder","year":2024,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Numerical Analysis Techniques","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Remainder; Arc (geometry); Planarity testing; Combinatorics; Mathematics; Arithmetic; Geometry","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":[],"consensus_categories":[],"category_scores_codex":[0.00007135487,0.00022625,0.0004634852,0.0003022761,0.00002310687,0.00000785062,0.0003715006,0.0001703042,0.00003384239],"category_scores_gemma":[0.000008591632,0.0002278295,0.0001700828,0.0006425483,0.0001746035,0.00005558727,0.0002456415,0.0005536068,0.00001077627],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001326082,"about_ca_system_score_gemma":0.00004507417,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000110134,"about_ca_topic_score_gemma":0.00007116303,"domain_scores_codex":[0.9991218,0.00002738501,0.0002362701,0.0003759353,0.00008024502,0.0001583833],"domain_scores_gemma":[0.9988909,0.00006980106,0.0001438162,0.0007053807,0.0001151056,0.00007497264],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00003621266,0.00008958431,0.001306541,0.0008750765,0.0006129335,0.00005538001,0.0001433771,0.9669133,0.001305779,0.02803773,0.0004661,0.0001579268],"study_design_scores_gemma":[0.0004424145,0.0001424242,0.004304358,0.001075783,0.001599218,0.00001055822,0.0004809169,0.7854598,0.01489292,0.1888856,0.00144993,0.001256051],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5524132,0.0001539579,0.4389593,0.00003043061,0.00009808238,0.000274029,0.000144926,0.0006441004,0.007282027],"genre_scores_gemma":[0.996373,0.0001419609,0.003132236,0.000004750164,0.00001274281,0.000001106698,0.00003517202,0.0000338026,0.0002652433],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4439598,"threshold_uncertainty_score":0.9290618,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04895455346339598,"score_gpt":0.1864057615323861,"score_spread":0.1374512080689902,"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."}}