{"id":"W4403322325","doi":"10.48550/arxiv.2410.03975","title":"Harmonic functions with highly intersecting zero sets","year":2024,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"Courtois Foundation","keywords":"Transcendental number; Counterexample; Ball (mathematics); Zero (linguistics); Mathematics; RADIUS; Harmonic function; Context (archaeology); Harmonic; Harmonic map; Mathematical analysis; Combinatorics; Pure mathematics; Physics; Computer science; Acoustics; Philosophy; Geography","routes":{"ca_aff":true,"ca_fund":true,"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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0002867007,0.0004128141,0.0005220189,0.0007024649,0.0001639772,0.0001555092,0.0004823752,0.000339776,0.0002565783],"category_scores_gemma":[0.00009463028,0.0003697924,0.0004280113,0.001674599,0.00007684995,0.000101909,0.000998057,0.001395206,0.0003514515],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002871911,"about_ca_system_score_gemma":0.0001604075,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001398599,"about_ca_topic_score_gemma":0.0002527806,"domain_scores_codex":[0.9981793,0.00008286265,0.0002578509,0.0009830453,0.0001377493,0.0003592135],"domain_scores_gemma":[0.9982858,0.0002201058,0.0002652136,0.0008761839,0.0002009505,0.0001517038],"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":[0.0005945364,0.001619057,0.01187197,0.004939684,0.01647151,0.005662505,0.004267969,0.1495001,0.0001727344,0.6809222,0.1194998,0.004477924],"study_design_scores_gemma":[0.001476143,0.0003476887,0.0006686678,0.001713707,0.009250579,0.00005455061,0.005099334,0.1203041,0.0001422717,0.8513033,0.007185111,0.002454472],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8927239,0.0001915361,0.09260879,0.0001189488,0.0007361985,0.0002793225,0.00004093324,0.0003989506,0.01290145],"genre_scores_gemma":[0.9806879,0.00004009348,0.0006274886,0.00003309265,0.0001019947,0.000001960135,0.00003675716,0.00005885292,0.01841188],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1703811,"threshold_uncertainty_score":0.9998754,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09391670318461243,"score_gpt":0.2113520960346753,"score_spread":0.1174353928500629,"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."}}