{"id":"W4412475627","doi":"10.28924/2291-8639-23-2025-162","title":"On the Negative Spectrum of One-Dimensional Schrödinger Operators on Quantum Trees with Point Interactions","year":2025,"lang":"en","type":"article","venue":"International Journal of Analysis and Applications","topic":"advanced mathematical theories","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Spectrum (functional analysis); Schrödinger's cat; Point (geometry); Quantum; Pure mathematics; Mathematical physics; Quantum mechanics; Physics; Geometry","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":[0.0002969549,0.0001105027,0.0002930867,0.0004297352,0.0001053882,0.00004395556,0.0002591405,0.00002236858,0.0001513488],"category_scores_gemma":[0.0003955847,0.00006353937,0.0001675202,0.0005143591,0.0001563801,0.0001024093,0.00004425758,0.000203931,0.000003147768],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000570606,"about_ca_system_score_gemma":0.00004482759,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005643216,"about_ca_topic_score_gemma":0.00003222637,"domain_scores_codex":[0.9988894,0.00005028252,0.000476676,0.0001246069,0.0003845252,0.0000744489],"domain_scores_gemma":[0.9964361,0.002415401,0.0004515733,0.000193948,0.0004646902,0.00003825017],"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":[0.000119367,0.0003687084,0.0001194265,0.000004937631,0.002105823,0.000001065677,0.0001261129,0.0009830573,0.0004967267,0.9951324,0.0002033971,0.0003389929],"study_design_scores_gemma":[0.0002999226,0.0001162735,0.0007010695,0.0002138456,0.0006110595,0.000007629387,0.0005845827,0.001134931,0.01034848,0.9856071,0.0002988969,0.00007623125],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5093263,0.00004199274,0.4674477,0.01681549,0.00008908207,0.0003263485,0.00005034701,0.00001709895,0.005885662],"genre_scores_gemma":[0.993042,0.00001914579,0.006376444,0.0002231415,0.00005691259,0.0000248975,0.000001930747,0.000007031008,0.0002485118],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4837157,"threshold_uncertainty_score":0.259106,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02014236798969581,"score_gpt":0.3387715489917614,"score_spread":0.3186291810020656,"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."}}