{"id":"W4385291900","doi":"10.48550/arxiv.2307.13112","title":"External columns and chambers of vector partition functions","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Universidad de Sevilla","keywords":"Combinatorics; Partition (number theory); Partition function (quantum field theory); Mathematics; Polynomial; Piecewise; Enumeration; Binomial theorem; Function (biology); Binomial coefficient; Discrete mathematics; Physics; Mathematical analysis; Quantum mechanics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004842585,0.0003790346,0.0003432766,0.001019933,0.0008325073,0.002069074,0.000503843,0.0003834292,0.006633442],"category_scores_gemma":[0.002299401,0.0003493122,0.000481599,0.0008346627,0.001600834,0.002373761,0.001368574,0.0009450403,0.0006394936],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008422313,"about_ca_system_score_gemma":0.0004197341,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001365373,"about_ca_topic_score_gemma":0.001282968,"domain_scores_codex":[0.9994081,0.0001255037,0.00002302396,0.0001108553,0.0001555379,0.0001769611],"domain_scores_gemma":[0.9987959,0.0005357864,0.0001618176,0.000134455,0.0001904339,0.0001816653],"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":[0.00003764066,0.00001281633,0.0008775163,0.00002753991,0.000003991052,0.00005415212,0.0001435517,0.002292857,0.002819298,0.9875413,0.0005311995,0.005658141],"study_design_scores_gemma":[0.00003487971,0.00007827634,0.002796347,0.00004883403,0.00002159455,0.0003574013,0.0003033927,0.08401108,0.01320453,0.8858114,0.01328917,0.00004303189],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7258391,0.0004782788,0.2203605,0.000410511,0.00006340765,0.00005317365,0.0004791913,0.0003394433,0.05197642],"genre_scores_gemma":[0.9696354,0.0002332409,0.01748901,0.00008573665,0.00006026858,0.0000512903,0.0003415924,0.0001375059,0.01196597],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006633442,"threshold_uncertainty_score":0.02219105,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1779105333994108,"score_gpt":0.2384620535813782,"score_spread":0.06055152018196741,"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."}}