{"id":"W4417521212","doi":"10.48550/arxiv.2504.17831","title":"Decomposition of Borel graphs and cohomology","year":2025,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Japan Society for the Promotion of Science; McGill University","keywords":"Borel equivalence relation; Borel set; Bounded function; Lipschitz continuity; Graph; Borel hierarchy","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":[0.0004693081,0.000311671,0.0003106164,0.001988097,0.0007678571,0.001300894,0.0005325386,0.0005246306,0.004694055],"category_scores_gemma":[0.001696741,0.0002105797,0.0005344666,0.0006239821,0.002350457,0.002842393,0.002126617,0.001552603,0.0002560631],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001098226,"about_ca_system_score_gemma":0.0002471836,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009696453,"about_ca_topic_score_gemma":0.0008211307,"domain_scores_codex":[0.9996049,0.00007008097,0.00001227062,0.00009364679,0.0001077219,0.0001113988],"domain_scores_gemma":[0.9988449,0.0003676242,0.0001165291,0.0001348177,0.0002182895,0.0003177929],"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":[0.00001193344,0.00001103975,0.0008597804,0.00001949435,0.000005166301,0.00004818966,0.0002515015,0.000815289,0.001918453,0.9926274,0.000385488,0.003046358],"study_design_scores_gemma":[0.000009291763,0.00002269648,0.002525691,0.00001759333,0.000009154795,0.0001343977,0.0002633799,0.0101305,0.001287855,0.9820057,0.003582966,0.00001072834],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"other","genre_scores_codex":[0.7655466,0.001073898,0.1749669,0.002126894,0.0001044345,0.00003781779,0.0002728652,0.0001762039,0.05569445],"genre_scores_gemma":[0.9874142,0.0002271073,0.008092653,0.0001164752,0.00006763157,0.00002009925,0.0001477546,0.00002166129,0.003892306],"genre_candidate":"other","genre_consensus":null,"teacher_disagreement_score":0.004694055,"threshold_uncertainty_score":0.01570314,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07504702704652329,"score_gpt":0.237538260674613,"score_spread":0.1624912336280898,"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."}}