{"id":"W2022467326","doi":"10.1007/s00454-001-0038-7","title":"Locked and Unlocked Polygonal Chains in Three Dimensions","year":2001,"lang":"en","type":"article","venue":"Discrete & Computational Geometry","topic":"Computational Geometry and Mesh Generation","field":"Computer Science","cited_by":36,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University; University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada; McGill University; National Science Foundation","keywords":"Polygonal chain; Combinatorics; Mathematics; Regular polygon; Convex polygon; Simple (philosophy); Chain (unit); Polygon (computer graphics); Plane (geometry); Planar; Polytope; Convex polytope; Simple polygon; Projection (relational algebra); Geometry; Convex set; Algorithm; Computer science; Convex optimization; Computer graphics (images)","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0003618738,0.0002446525,0.0002503786,0.000824552,0.0002486881,0.0001723407,0.0003907646,0.00009075938,0.00004843656],"category_scores_gemma":[0.00008789342,0.0002496954,0.00007851642,0.00213253,0.00008912144,0.0005829674,0.0003085332,0.0002206441,0.00005063458],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007202214,"about_ca_system_score_gemma":0.0001530333,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000410741,"about_ca_topic_score_gemma":0.00005946698,"domain_scores_codex":[0.9978648,0.00008035875,0.0004375331,0.0006293139,0.0005933333,0.0003946609],"domain_scores_gemma":[0.9988704,0.000387936,0.0001143863,0.0002694862,0.0001619203,0.0001958193],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00006390816,0.0002740203,0.04549062,0.00002339145,0.00007019196,0.0001249715,0.0005890211,0.3198875,0.0004236932,0.5937101,0.0003320281,0.0390106],"study_design_scores_gemma":[0.0008268754,0.00007759535,0.2926776,0.00002512815,0.000005899739,0.0001186696,0.00003650084,0.6370692,0.00003111379,0.06793947,0.000884559,0.0003073413],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.494498,0.0003573077,0.5028656,0.001374416,0.0001956919,0.0001564191,0.000007912282,0.00008437352,0.0004602738],"genre_scores_gemma":[0.9585799,0.00002764336,0.04018155,0.0007340426,0.0001221172,0.00002095163,0.0001093787,0.00001361297,0.0002108012],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5257706,"threshold_uncertainty_score":0.9999955,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01483621241296793,"score_gpt":0.2540274448580924,"score_spread":0.2391912324451244,"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."}}