{"id":"W4380877822","doi":"10.1007/s13398-023-01467-x","title":"Linked partition ideals and Euclidean billiard partitions","year":2023,"lang":"es","type":"article","venue":"Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"Dalhousie University","funders":"Killam Trusts","keywords":"Dynamical billiards; Partition (number theory); Mathematics; Euclidean geometry; Euclidean space; Combinatorics; Invariant (physics); Integer (computer science); Euclidean distance; Pure mathematics; Geometry; Computer science; Mathematical physics","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":[0.0006654984,0.0005525176,0.0008340668,0.002470942,0.002271762,0.004109038,0.000991811,0.001097021,0.007768736],"category_scores_gemma":[0.001991304,0.0005208413,0.0007928643,0.001723222,0.00390645,0.004203292,0.002339388,0.003317092,0.0007746081],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001544386,"about_ca_system_score_gemma":0.0005426776,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001104382,"about_ca_topic_score_gemma":0.0009502627,"domain_scores_codex":[0.9993943,0.0001606418,0.00002724503,0.0001133377,0.00017338,0.0001310665],"domain_scores_gemma":[0.9992713,0.000273499,0.0001274835,0.00008575354,0.00008867442,0.0001533185],"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":[0.00001055584,0.000005646074,0.0000477688,0.000007589592,0.000002129338,0.00001416597,0.00006737592,0.0001627719,0.00009933027,0.9985847,0.0003039526,0.0006940292],"study_design_scores_gemma":[0.00001623005,0.000006976065,0.000251326,0.000008368932,0.000005614222,0.0000658469,0.0001010328,0.001010562,0.0001550314,0.9951808,0.003191274,0.000006933657],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5987504,0.004936796,0.07284122,0.00515015,0.001155965,0.00007197684,0.0004298253,0.0001978613,0.3164659],"genre_scores_gemma":[0.9468009,0.001540089,0.009848904,0.0005233724,0.0007738109,0.00006677903,0.0003783279,0.00008184881,0.03998585],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007768736,"threshold_uncertainty_score":0.02598906,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02837015505728931,"score_gpt":0.3500534185069198,"score_spread":0.3216832634496305,"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."}}