{"id":"W4414684974","doi":"","title":"Inverse problems for the Bakry-\\'Emery Laplacian on manifolds with boundary -- uniqueness and non-uniqueness","year":2025,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Advanced Mathematical Modeling in Engineering","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"","keywords":"Uniqueness; Boundary (topology); Manifold (fluid mechanics); Laplace operator; Metric (unit); Riemannian manifold; Inverse problem; Statistical manifold","routes":{"ca_aff":true,"ca_fund":false,"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":[0.0004548313,0.0004491168,0.0004372684,0.0001157173,0.0002719804,0.0001953548,0.001320405,0.0002468567,0.000001457313],"category_scores_gemma":[0.0000860355,0.0003210819,0.00009195208,0.0002344959,0.0001311321,0.0002378262,0.001180319,0.0006707997,0.000004763371],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001141478,"about_ca_system_score_gemma":0.0002536427,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003033515,"about_ca_topic_score_gemma":0.00004238581,"domain_scores_codex":[0.9980889,0.00003971545,0.0003583075,0.0008331512,0.0002558237,0.000424101],"domain_scores_gemma":[0.9975812,0.0005737118,0.0001635197,0.001408887,0.0001663973,0.0001063115],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00009817759,0.000227903,0.005234574,0.005789213,0.0004068332,0.00005090538,0.002624106,0.8792247,0.0004141601,0.0985737,0.0003547104,0.007001],"study_design_scores_gemma":[0.0007026577,0.0002073137,0.002455313,0.002984085,0.000109902,0.00001712913,0.00006498518,0.9359797,0.002087134,0.05174488,0.002647799,0.0009991362],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.07290711,0.0001393637,0.9235076,0.0008444617,0.0005420496,0.001232961,0.00001363903,0.0003035525,0.0005092836],"genre_scores_gemma":[0.7631992,0.0001867653,0.2330829,0.001137772,0.000175569,0.001341469,0.00001377596,0.0000841223,0.0007784584],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.6904247,"threshold_uncertainty_score":0.9999241,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03361715497083496,"score_gpt":0.2640779105661489,"score_spread":0.230460755595314,"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."}}