{"id":"W4417029034","doi":"10.48550/arxiv.2512.03412","title":"Fourier coefficients of Eisenstein series on ${\\rm SO}(3,n+1)$","year":2025,"lang":"","type":"preprint","venue":"ArXiv.org","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Lift (data mining); Type (biology); Cusp (singularity); Infinity; Group (periodic table); Construct (python library)","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","insufficient_payload"],"consensus_categories":["metaepi_narrow"],"category_scores_codex":[0.0006768676,0.001276821,0.002113934,0.0007188981,0.0004601011,0.00008054213,0.001246004,0.001081802,0.0009633256],"category_scores_gemma":[0.001963763,0.001282174,0.001105299,0.001072444,0.0008089943,0.0002026874,0.001919778,0.001758183,0.000728565],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002378129,"about_ca_system_score_gemma":0.0005972133,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001293215,"about_ca_topic_score_gemma":0.00001688852,"domain_scores_codex":[0.9938697,0.000260486,0.002086068,0.001615205,0.001074888,0.001093623],"domain_scores_gemma":[0.9933006,0.001091078,0.001510438,0.003112066,0.0006800762,0.0003057387],"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":[0.004665262,0.01632696,0.2424536,0.04217648,0.009234628,0.0006448102,0.01838063,0.01820404,0.007166357,0.5395964,0.009806986,0.09134386],"study_design_scores_gemma":[0.01151338,0.003884682,0.03370543,0.03113218,0.005250643,0.00007450894,0.009740164,0.001958346,0.3536713,0.433228,0.1060115,0.009829845],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9703464,0.0007851435,0.009533053,0.0005601574,0.003502683,0.001453453,0.0004529801,0.0001741052,0.01319204],"genre_scores_gemma":[0.9453944,0.0006340299,0.005565001,0.0003705717,0.0004467671,0.00008733696,0.00008675885,0.0001358752,0.04727928],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3465049,"threshold_uncertainty_score":0.9999984,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.047974239146708,"score_gpt":0.3188938119758977,"score_spread":0.2709195728291897,"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."}}