{"id":"W7217664","doi":"10.4169/math.mag.85.5.343","title":"From Polygons to String Theory","year":2012,"lang":"en","type":"article","venue":"Mathematics Magazine","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"Bard College; Harvey Mudd College; National Science Foundation","keywords":"Polytope; Mathematics; Reflexivity; Fano plane; Duality (order theory); Mirror symmetry; String (physics); Combinatorics; Connection (principal bundle); Pure mathematics; Algebra over a field; Theoretical physics; Geometry; Physics; Mathematical physics","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","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.00108977,0.0004529376,0.0006886327,0.000186688,0.0001373199,0.0000693465,0.0005900005,0.0001525571,0.0007176108],"category_scores_gemma":[0.002518492,0.0004084881,0.000160763,0.0004520172,0.00005683499,0.0003255737,0.00041158,0.0002926296,0.00270845],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001502484,"about_ca_system_score_gemma":0.00002934206,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002756463,"about_ca_topic_score_gemma":0.000002457856,"domain_scores_codex":[0.9972969,0.00009617137,0.0008064181,0.0003201107,0.0006033624,0.0008769989],"domain_scores_gemma":[0.9953908,0.002409089,0.0003046203,0.001280266,0.0001204921,0.0004947798],"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":[0.00001627577,0.000729413,0.00005619002,0.0001644325,0.000108243,0.000004489525,0.006520833,0.000003772031,0.004529504,0.9813223,0.005639447,0.0009050294],"study_design_scores_gemma":[0.0004535285,0.0000478795,0.00006119236,0.0001829184,0.0001708209,0.0000158861,0.0008116658,0.00009716047,0.005864851,0.9875084,0.004294639,0.0004910783],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.4520044,0.0002177922,0.5088524,0.0004126884,0.00186689,0.00124088,0.00007664482,0.0009311331,0.03439714],"genre_scores_gemma":[0.4375264,0.000004293868,0.5560232,0.0001835489,0.001136279,0.0001073524,0.000009046653,0.0001905508,0.004819356],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.04717076,"threshold_uncertainty_score":0.9998367,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04765814578117171,"score_gpt":0.3322840173334154,"score_spread":0.2846258715522437,"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."}}