{"id":"W7097965695","doi":"","title":"Previous Up Next Article Citations From References: 4 From Reviews: 0","year":2013,"lang":"en","type":"article","venue":"","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Congruence relation; Modulo; Congruence (geometry); Legendre polynomials; Prime (order theory); Legendre's equation","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":false,"about_ca":true,"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":[0.0001279225,0.0001872645,0.0004117426,0.00003678112,0.00008912059,0.0001875972,0.0002720383,0.00007344491,0.01823138],"category_scores_gemma":[0.001858304,0.000140149,0.0001011134,0.0001410427,0.00007958384,0.000802134,0.00009391414,0.0001355376,0.008290181],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003711728,"about_ca_system_score_gemma":0.00001614086,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006843204,"about_ca_topic_score_gemma":0.0002594344,"domain_scores_codex":[0.9985124,0.00009044378,0.0006229975,0.0002800826,0.000236851,0.0002571684],"domain_scores_gemma":[0.9974666,0.001492425,0.0001701221,0.0006236007,0.0001172687,0.0001299369],"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":[0.000008426196,0.0005082029,0.0004685662,0.0003095536,0.000200109,0.000004622622,0.007643098,0.000002582926,0.01054865,0.7122888,0.2523929,0.01562446],"study_design_scores_gemma":[0.0001938293,0.00001495795,0.0003063699,0.0001773501,0.00006297525,4.544793e-7,0.001492712,0.000427268,0.00123929,0.9935691,0.00232733,0.0001884065],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"methods","genre_scores_codex":[0.7963616,0.002874811,0.1284372,0.001075499,0.0004651106,0.002085317,0.00005479684,0.0007459501,0.06789977],"genre_scores_gemma":[0.3278548,0.0009026964,0.6186185,0.0006298919,0.0002738224,0.000716546,0.000043367,0.00007582502,0.05088454],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.4901814,"threshold_uncertainty_score":0.992482,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.176319371420085,"score_gpt":0.3606728480150538,"score_spread":0.1843534765949688,"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."}}