{"id":"W4408160643","doi":"10.1017/fms.2025.10","title":"Elliptic Pre-Complexes, Hodge-like Decompositions and Overdetermined Boundary-Value Problems","year":2025,"lang":"en","type":"article","venue":"Forum of Mathematics Sigma","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Azrieli Foundation; Israel Science Foundation","keywords":"Mathematics; Overdetermined system; Boundary value problem; Value (mathematics); Pure mathematics; Boundary (topology); Elliptic curve; Algebra over a field; Mathematical analysis; Statistics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001481538,0.0006085745,0.0005688599,0.001655831,0.001407363,0.00266623,0.0008132189,0.001172397,0.004292056],"category_scores_gemma":[0.004112528,0.0004038648,0.0005435673,0.0005478168,0.004124899,0.003990008,0.002648706,0.002105911,0.000332364],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001464685,"about_ca_system_score_gemma":0.0005842792,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008467214,"about_ca_topic_score_gemma":0.0005442921,"domain_scores_codex":[0.9991974,0.0002180344,0.00004295936,0.0001417091,0.0002781613,0.0001217208],"domain_scores_gemma":[0.9985991,0.0003709585,0.0002812009,0.0001445346,0.0002690605,0.0003351434],"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":[0.000007675338,0.000009110518,0.000252063,0.000009053527,0.000003290121,0.00008358077,0.000170893,0.001187539,0.0003782862,0.99632,0.0002148993,0.001363541],"study_design_scores_gemma":[0.000007073532,0.000009501718,0.0003160304,0.00001312945,0.000002309162,0.0001204468,0.000152205,0.01361469,0.0005334988,0.9834186,0.001802584,0.0000100225],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.706129,0.000876167,0.2472399,0.002017336,0.0001995933,0.00009021351,0.00009997598,0.00009934111,0.04324842],"genre_scores_gemma":[0.954994,0.0002977889,0.03389318,0.0001846097,0.0001439077,0.00004846305,0.0001058377,0.00005695126,0.01027532],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004292056,"threshold_uncertainty_score":0.01435828,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01497027426940264,"score_gpt":0.2849159369467099,"score_spread":0.2699456626773072,"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."}}