{"id":"W2591601825","doi":"10.1007/s00039-015-0320-0","title":"Arcs intersecting at most once","year":2015,"lang":"en","type":"article","venue":"Geometric and Functional Analysis","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":27,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Pairwise comparison; Cardinality (data modeling); Combinatorics; Euler characteristic; Set (abstract data type); Bounded function; Surface (topology); Simple (philosophy); Polynomial; Boundary (topology); Euler's formula; Jordan curve theorem; Discrete mathematics; Geometry; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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":[],"consensus_categories":[],"category_scores_codex":[0.0005632162,0.0008295177,0.001098765,0.001478077,0.00153845,0.001504012,0.001175521,0.0005949124,0.00484039],"category_scores_gemma":[0.004703671,0.0005767373,0.001071094,0.0009257892,0.002052859,0.002811434,0.003353662,0.001832912,0.0007040707],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008790445,"about_ca_system_score_gemma":0.0005022522,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007832775,"about_ca_topic_score_gemma":0.0008169042,"domain_scores_codex":[0.9984383,0.0001710693,0.0001111482,0.0004719451,0.0005280659,0.0002793659],"domain_scores_gemma":[0.9946585,0.001927104,0.001090921,0.001035149,0.0006095645,0.0006787585],"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":[0.0009272277,0.0001478231,0.01853617,0.0006650421,0.0001863012,0.002093167,0.001242734,0.06011648,0.07924356,0.7595872,0.003804807,0.07344947],"study_design_scores_gemma":[0.00004716116,0.0002711418,0.01541306,0.0001867285,0.0001575657,0.005418544,0.0009297217,0.1648895,0.07998765,0.7017042,0.03086703,0.0001276556],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7713725,0.0006220431,0.1859492,0.0003846536,0.0001276024,0.00004853681,0.0007459038,0.0003681238,0.04038136],"genre_scores_gemma":[0.949412,0.0003793289,0.04287989,0.00006376001,0.00009474816,0.00006298744,0.0006890575,0.0001508445,0.006267371],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00484039,"threshold_uncertainty_score":0.01619273,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08443067350045641,"score_gpt":0.2840017176295363,"score_spread":0.1995710441290799,"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."}}