{"id":"W1660287306","doi":"10.1007/978-1-4020-9927-4_2","title":"Lattice Polygons and Related Objects","year":2009,"lang":"en","type":"book-chapter","venue":"Lecture notes in physics","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Ising model; Polygon (computer graphics); Lattice (music); Combinatorics; Monte Carlo method; Perimeter; Regular polygon; Exponential function; Physics; Constraint (computer-aided design); Statistical physics; Mathematics; Geometry; Mathematical analysis; Computer science; Statistics","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":[0.0001027845,0.0003997011,0.0006158531,0.000187908,0.00005772289,0.00002009062,0.0001619188,0.0007131034,0.0001703351],"category_scores_gemma":[0.0004122142,0.0003696499,0.0001166324,0.0001620532,0.0001400612,0.00003863756,0.00007848884,0.001006861,0.00005033198],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005408802,"about_ca_system_score_gemma":0.00005673323,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009557305,"about_ca_topic_score_gemma":0.00002880445,"domain_scores_codex":[0.9987317,0.00002400351,0.0003322432,0.0004061896,0.0001928265,0.0003130764],"domain_scores_gemma":[0.9983092,0.0009495403,0.0002203311,0.0004093786,0.00004344263,0.00006812319],"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":[0.0000108726,0.00005153159,0.000018291,0.0001059401,0.00008121543,0.00008263214,0.0007622527,0.00001904353,0.00001846902,0.8147347,0.0002218606,0.1838932],"study_design_scores_gemma":[0.000322086,0.00008505602,0.00003554054,0.0001392445,0.0001246426,0.00004329132,0.000002586786,0.00003635037,0.0001117841,0.9953855,0.003353297,0.0003606652],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.001810941,0.004872307,0.006366811,0.001035272,0.0006300426,0.0006917683,0.00003976881,0.000279969,0.9842731],"genre_scores_gemma":[0.8131172,0.0007519505,0.01551877,0.001653724,0.001663325,0.00001203652,0.0001027115,0.0003488233,0.1668314],"genre_candidate":"other","genre_consensus":null,"teacher_disagreement_score":0.8174416,"threshold_uncertainty_score":0.9998755,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02181910485081209,"score_gpt":0.2645957287527358,"score_spread":0.2427766239019237,"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."}}