{"id":"W4416452333","doi":"10.48550/arxiv.2505.16564","title":"Graph splitting methods: Fixed points and strong convergence for linear subspaces","year":2025,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Advanced Optimization Algorithms Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Agencia Estatal de Investigación; European Social Fund; European Regional Development Fund; Natural Sciences and Engineering Research Council of Canada","keywords":"Linear subspace; Fixed point; Graph; Monotone polygon; Linear operators; Linear map; Graph theory","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.001407165,0.0003752162,0.0006305352,0.0002617332,0.0002177925,0.00005792423,0.0004635544,0.0003336751,0.0000979711],"category_scores_gemma":[0.00506837,0.0003788598,0.0001781741,0.0002805636,0.000158025,0.0001298122,0.001066746,0.0007298448,0.000008139345],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008406705,"about_ca_system_score_gemma":0.0001983604,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001787378,"about_ca_topic_score_gemma":0.00001608537,"domain_scores_codex":[0.9975321,0.0002856658,0.0005981416,0.0008140284,0.0002794943,0.0004905309],"domain_scores_gemma":[0.995654,0.002571198,0.0003774864,0.0007315696,0.0005172179,0.0001485556],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.001278593,0.001871803,0.6206686,0.0532998,0.006049624,0.0001143473,0.01658186,0.03389641,0.004073961,0.1524409,0.009576575,0.1001475],"study_design_scores_gemma":[0.004153906,0.0002392886,0.007051573,0.002936122,0.0006876797,0.00001205417,0.003500869,0.5550149,0.04071326,0.3773456,0.005535232,0.002809482],"study_design_candidate":"observational","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.06429202,0.0005452322,0.931986,0.0005903947,0.0004869459,0.001434369,0.0001306268,0.0001916975,0.0003427417],"genre_scores_gemma":[0.004153018,0.0005628759,0.9908615,0.000069014,0.0001552772,0.0002960883,0.00005797804,0.00006193302,0.003782253],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.613617,"threshold_uncertainty_score":0.9998663,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1897718242364822,"score_gpt":0.4788410518948429,"score_spread":0.2890692276583607,"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."}}