{"id":"W7091186422","doi":"","title":"Generalized Rank via Minimal Subposet","year":2025,"lang":"en","type":"article","venue":"ArXiv.org","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"","keywords":"Embedding; Subcategory; Invariant (physics); Partially ordered set; Property (philosophy); Multiplicity (mathematics)","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":[],"consensus_categories":[],"category_scores_codex":[0.0001320637,0.0001885069,0.0003048962,0.0000652723,0.0001240763,0.00002565679,0.0002841958,0.0001390105,0.0002828472],"category_scores_gemma":[0.0001441927,0.0001634653,0.0001389292,0.0002074661,0.00004005291,0.00006728947,0.0001144548,0.0001557528,0.00005929603],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004152397,"about_ca_system_score_gemma":0.00005549073,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004660464,"about_ca_topic_score_gemma":0.00001078697,"domain_scores_codex":[0.9989051,0.00005915134,0.0003030672,0.000277233,0.0001673283,0.0002881149],"domain_scores_gemma":[0.9991757,0.0001569349,0.00008041668,0.000455395,0.00006733433,0.00006416206],"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":[0.0001238167,0.00009033144,0.05772329,0.00007782407,0.0001594086,0.00001383232,0.0002754796,0.000002677094,0.002860065,0.9240477,0.01391867,0.0007069076],"study_design_scores_gemma":[0.001713296,0.00004691239,0.02019279,0.0000331166,0.00009622837,0.000004349396,0.00003807307,0.0001581818,0.006495968,0.9642385,0.00672689,0.0002557037],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9932001,0.0002027766,0.001337801,0.0005526125,0.001362226,0.0002027558,0.000002982873,0.0001275697,0.003011124],"genre_scores_gemma":[0.9949895,0.00001290578,0.0008767847,0.000536355,0.0002311516,0.00002555534,0.000005851787,0.00002308603,0.003298879],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04019081,"threshold_uncertainty_score":0.6665921,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03944148644289221,"score_gpt":0.3039729558894123,"score_spread":0.2645314694465201,"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."}}