{"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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0001788154,0.0002168446,0.0003905934,0.0001185283,0.0001070217,0.00002591445,0.0002242067,0.0002235989,0.00004650567],"category_scores_gemma":[0.0002603186,0.0002683815,0.0001338916,0.0002537217,0.0001773141,0.00009845658,0.0005427337,0.0003390121,0.00003657405],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001297829,"about_ca_system_score_gemma":0.00008209056,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005394614,"about_ca_topic_score_gemma":0.00006138873,"domain_scores_codex":[0.9989377,0.00006603654,0.0002611875,0.0004362781,0.00009564553,0.0002031334],"domain_scores_gemma":[0.9983795,0.0003987805,0.000395245,0.0005782768,0.0001461868,0.0001020278],"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":[0.00007636387,0.0002552999,0.001792265,0.001125089,0.0002219026,0.0001028198,0.000629973,0.0100424,0.0002331468,0.9845664,0.0008876814,0.00006668675],"study_design_scores_gemma":[0.0004699206,0.00006252819,0.0005180722,0.0003942964,0.0002446916,0.000002940355,0.0002623239,0.01460474,0.0001610638,0.982959,0.00006266557,0.0002577612],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.872061,0.00001797964,0.12557,0.0000281132,0.0009831467,0.0004037307,0.00006930602,0.0002359908,0.0006306821],"genre_scores_gemma":[0.9945427,0.00007136331,0.002502848,0.000004091476,0.00007044567,0.000003163413,0.000009478936,0.00004529101,0.002750642],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1230672,"threshold_uncertainty_score":0.9999768,"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."}}