{"id":"W4416781455","doi":"10.48550/arxiv.2511.21656","title":"Simple proofs of discretised projection theorems","year":2025,"lang":"","type":"preprint","venue":"ArXiv.org","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Projection (relational algebra); Mathematical proof; Simple (philosophy); Lebesgue measure; Lebesgue integration; Measure (data warehouse); Polynomial; Set (abstract data type)","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","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001549145,0.0009470354,0.001969542,0.0003354793,0.0002304232,0.0001001935,0.001030518,0.001018633,0.001436485],"category_scores_gemma":[0.002295197,0.0008203796,0.0008969249,0.0005817159,0.0004554043,0.0001551988,0.001496484,0.001335155,0.0001297941],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001904545,"about_ca_system_score_gemma":0.0004816952,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001298296,"about_ca_topic_score_gemma":0.00004483684,"domain_scores_codex":[0.9944279,0.0003536716,0.002489361,0.001194182,0.0007604939,0.0007744554],"domain_scores_gemma":[0.9939012,0.001297912,0.001788032,0.00222388,0.0005744293,0.0002145716],"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":[0.0003766504,0.004404447,0.0677731,0.03412602,0.001715707,0.0000221425,0.005390181,0.0001227987,0.003644848,0.8726805,0.0008750454,0.008868503],"study_design_scores_gemma":[0.001147741,0.0003124275,0.009832545,0.00372648,0.0009962902,0.000008165928,0.000699538,0.06395629,0.005201803,0.9114624,0.001450697,0.001205602],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8309652,0.0001952417,0.08393329,0.0004219804,0.001061261,0.005164139,0.0005667523,0.0001900235,0.07750215],"genre_scores_gemma":[0.9841112,0.0002781115,0.004241901,0.00006492626,0.000242251,0.0004022747,0.0001603227,0.0001039433,0.01039508],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.153146,"threshold_uncertainty_score":0.9994763,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.058383843586302,"score_gpt":0.3364930528759291,"score_spread":0.2781092092896271,"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."}}