{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008611562,0.0008723684,0.00083332,0.002219081,0.001544244,0.002862688,0.001037705,0.0008991722,0.00483037],"category_scores_gemma":[0.005828662,0.0005004735,0.0004948989,0.0007736311,0.003495244,0.003375236,0.003715492,0.001571402,0.0007952304],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00106491,"about_ca_system_score_gemma":0.0003637894,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005043824,"about_ca_topic_score_gemma":0.0003478518,"domain_scores_codex":[0.9994172,0.00008917646,0.00002450289,0.0001398144,0.000187095,0.0001422923],"domain_scores_gemma":[0.9976174,0.001035127,0.0004581182,0.0002572456,0.0002145521,0.0004175678],"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":[0.0001582099,0.00004777865,0.001496708,0.0001051656,0.0000253639,0.0004026458,0.0004481295,0.01205299,0.01104055,0.9613138,0.001176681,0.0117319],"study_design_scores_gemma":[0.00005042767,0.000132852,0.001627062,0.00005560688,0.00004603589,0.0008187702,0.0004735374,0.1117729,0.01962392,0.858393,0.006936098,0.00006988248],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8149636,0.0007619897,0.1478195,0.0005205041,0.000133447,0.00003183828,0.0001391414,0.0002459128,0.03538403],"genre_scores_gemma":[0.983348,0.0002908247,0.01030548,0.00005550815,0.00009861679,0.00002848189,0.00009336575,0.00008143413,0.005698382],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00483037,"threshold_uncertainty_score":0.01615918,"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."}}