{"id":"W4410568988","doi":"10.1017/s1446788725000096","title":"DIFFRACTION OF THE PRIMES AND OTHER SETS OF ZERO DENSITY","year":2025,"lang":"en","type":"article","venue":"Journal of the Australian Mathematical Society","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"MacEwan University; Mount Royal University","funders":"","keywords":"Mathematics; Zero (linguistics); Linguistics","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001617627,0.000114473,0.0004161524,0.00002256033,0.00009260242,0.00001803662,0.0004712488,0.0001140317,0.0001112786],"category_scores_gemma":[0.001051545,0.00005594157,0.0005448067,0.0002394443,0.000475052,0.00006510632,0.0002052453,0.0004226097,0.000001606468],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006509982,"about_ca_system_score_gemma":0.00009045867,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006280959,"about_ca_topic_score_gemma":0.000001206012,"domain_scores_codex":[0.9983745,0.0002032895,0.0006509962,0.00008178426,0.0005263066,0.000163097],"domain_scores_gemma":[0.9978006,0.0008853803,0.0006682713,0.0003984534,0.0001945559,0.00005272076],"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":[0.0002680909,0.002119887,0.06055136,0.006106012,0.003503702,0.000003581912,0.009426843,0.00002665786,0.04632437,0.7439027,0.1264867,0.00128011],"study_design_scores_gemma":[0.0004277694,0.00002951769,0.01227036,0.0006559414,0.0003290311,0.00004813795,0.0009854243,0.0001814433,0.02506009,0.9597019,0.0002470036,0.00006338852],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.992481,0.00001888112,0.002879262,0.003263418,0.00008778327,0.0002189901,0.000004835124,0.000004488911,0.001041357],"genre_scores_gemma":[0.9875153,0.000006393453,0.006040594,0.00009664566,0.00002341104,8.464916e-7,2.39131e-8,0.00001113318,0.006305669],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2157992,"threshold_uncertainty_score":0.2281231,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05707606493402514,"score_gpt":0.3702074256230258,"score_spread":0.3131313606890007,"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."}}