{"id":"W4403969777","doi":"10.55016/ojs/cdm.v19i2.72712","title":"Combinatorial proof of Girard-Waring formula","year":2024,"lang":"en","type":"article","venue":"Contributions to Discrete Mathematics","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Combinatorial proof; Mathematics; Combinatorics; Combinatorial analysis; Combinatorial algorithms","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":[],"consensus_categories":[],"category_scores_codex":[0.0001725876,0.000141017,0.0002691576,0.0000549706,0.0001214386,0.00006479987,0.0001751436,0.00003282666,0.0002085349],"category_scores_gemma":[0.00008395375,0.0001163959,0.0001451372,0.0003378422,0.0000654295,0.0001073165,0.0001080305,0.0001160059,0.00007574441],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003477769,"about_ca_system_score_gemma":0.00004982191,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003357064,"about_ca_topic_score_gemma":1.612492e-7,"domain_scores_codex":[0.9990442,0.000009971186,0.0003898061,0.0001711852,0.0001493467,0.0002354647],"domain_scores_gemma":[0.9991097,0.0002483809,0.00006498677,0.0003297993,0.0001380847,0.0001090588],"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":[0.000002200605,0.00009442952,0.000006538619,0.000105762,0.00005295145,2.803847e-7,0.0003065575,0.00008037344,0.0007488209,0.9966362,0.0002692663,0.001696664],"study_design_scores_gemma":[0.0001673037,0.00003166263,0.000002165602,0.000187723,0.00006493751,7.986578e-7,0.0002708041,0.005119061,0.01909859,0.9648411,0.01007442,0.000141468],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.00495678,0.0000591592,0.9702941,0.0004069422,0.0001544377,0.0005822395,0.0006121715,0.00008028731,0.02285391],"genre_scores_gemma":[0.9871967,6.384076e-7,0.01192785,0.000007235956,0.0002072808,0.0001982653,0.00004392218,0.00002269874,0.0003953626],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.98224,"threshold_uncertainty_score":0.4746487,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008893299956262939,"score_gpt":0.3094824492079608,"score_spread":0.3005891492516979,"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."}}