{"id":"W4415651320","doi":"10.1215/00127094-2025-0017","title":"Reciprocity obstructions in semigroup orbits in SL(2,Z)","year":2025,"lang":"","type":"article","venue":"Duke Mathematical Journal","topic":"semigroups and automata theory","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Saint Mary's University","funders":"","keywords":"Semigroup; Conjecture; Reciprocity (cultural anthropology); Algebraic number; Finite set; Rational number; Congruence (geometry); Hausdorff dimension","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000414204,0.0002949096,0.0003313298,0.0009004849,0.001077727,0.001287087,0.0002397607,0.0003368036,0.003307838],"category_scores_gemma":[0.002037313,0.000204336,0.0006151842,0.0003000259,0.001838496,0.001241729,0.001277117,0.0006759018,0.0003611951],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005537025,"about_ca_system_score_gemma":0.0003392046,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009495437,"about_ca_topic_score_gemma":0.0005614929,"domain_scores_codex":[0.9996526,0.00004581327,0.00002937093,0.00006384366,0.0001047584,0.0001036876],"domain_scores_gemma":[0.9988942,0.0004503201,0.0002330234,0.0001433018,0.00009463148,0.0001845108],"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":[0.0002070429,0.00004480615,0.005234497,0.00008201893,0.00001494757,0.001204676,0.001881806,0.005502391,0.01321802,0.9626425,0.0005963839,0.009370908],"study_design_scores_gemma":[0.00007970315,0.0002090192,0.00621095,0.00006008396,0.00002855046,0.001155462,0.0009828429,0.04411034,0.0118468,0.9261914,0.009056183,0.00006865031],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9625269,0.0001648835,0.02392681,0.0001226101,0.00003552709,0.00002492212,0.0000798711,0.0001104249,0.01300794],"genre_scores_gemma":[0.9917671,0.00007384588,0.005229986,0.00002191365,0.00002942144,0.00002663181,0.0001190425,0.00002746971,0.00270461],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003307838,"threshold_uncertainty_score":0.01106584,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01282990722605898,"score_gpt":0.273142923055323,"score_spread":0.260313015829264,"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."}}