{"id":"W4412647913","doi":"10.4153/s0008439525100921","title":"Hook length inequalities for <i>t</i> -regular partitions in the <i>t</i> -aspect","year":2025,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Hook; Combinatorics; Inequality; Pure mathematics; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.001415951,0.0003153355,0.0005563995,0.0003075563,0.0003156436,0.0001740452,0.000683428,0.0001613585,0.002255901],"category_scores_gemma":[0.004971557,0.000243395,0.0002192184,0.0004177974,0.000313808,0.0000804781,0.00005788169,0.000314261,0.0007839332],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000254219,"about_ca_system_score_gemma":0.0002761499,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000291119,"about_ca_topic_score_gemma":0.004433262,"domain_scores_codex":[0.9975237,0.0001749341,0.0008052043,0.0003639862,0.00031206,0.0008201002],"domain_scores_gemma":[0.9940335,0.004750825,0.00009935941,0.0007810689,0.0001208673,0.0002143343],"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":[0.000005888027,0.0001078093,0.000009082807,0.0005867467,0.00002401369,0.00001468311,0.0007087089,0.000003621018,0.00001089621,0.8883336,0.1100958,0.00009919068],"study_design_scores_gemma":[0.000426058,0.00002892303,0.00001252142,0.000323927,0.00006626077,0.00001246611,0.002375657,0.00009091217,0.0001488587,0.8760796,0.1202055,0.0002293325],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.05608984,0.00103283,0.1845629,0.1330285,0.0006041724,0.008850271,0.0005398153,0.0006064581,0.6146852],"genre_scores_gemma":[0.8197865,0.00005528579,0.0623471,0.0140356,0.0003997098,0.00495859,0.00006405015,0.0002078846,0.09814533],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7636966,"threshold_uncertainty_score":0.9999941,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04258993333826971,"score_gpt":0.3194883905114131,"score_spread":0.2768984571731434,"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."}}