{"id":"W4413612163","doi":"10.1017/s1446788725101146","title":"ON TOEPLITZ ALGEBRAS OF PRODUCT SYSTEMS","year":2025,"lang":"en","type":"article","venue":"Journal of the Australian Mathematical Society","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo; University of Victoria","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Toeplitz matrix; Mathematics; Pure mathematics; Algebra over a field; Product (mathematics); Geometry","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001108263,0.0001903623,0.0005902531,0.00003923925,0.0000911851,0.00003386263,0.0007502483,0.0001176394,0.00008544029],"category_scores_gemma":[0.002000474,0.0001113835,0.0006673401,0.0003308657,0.0002118361,0.00009576401,0.0001211302,0.0005755614,0.000009509844],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00015178,"about_ca_system_score_gemma":0.00009489672,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":7.409369e-7,"about_ca_topic_score_gemma":1.331823e-7,"domain_scores_codex":[0.997815,0.0001145935,0.001062491,0.0001461628,0.000614427,0.0002473233],"domain_scores_gemma":[0.9971839,0.0009680304,0.0008452579,0.0006841084,0.0002464823,0.00007223214],"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":[0.00001673544,0.000296337,0.0000860434,0.0009450163,0.0002578518,0.000001802137,0.0003577454,0.00005289739,0.0008894706,0.9440228,0.05295797,0.0001152708],"study_design_scores_gemma":[0.0003884943,0.00006380291,0.0001913322,0.001133011,0.0001583833,0.00003655034,0.000421352,0.00005874329,0.008824864,0.9875679,0.001055095,0.000100498],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9508356,0.0001877997,0.02664746,0.01139274,0.001962881,0.001076593,0.00001484374,0.00005581443,0.00782628],"genre_scores_gemma":[0.9273786,0.00001263012,0.05323242,0.0002190338,0.000258891,0.000007717304,1.8372e-7,0.00003266363,0.01885786],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05190288,"threshold_uncertainty_score":0.4542088,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04825095668723247,"score_gpt":0.3464276891127596,"score_spread":0.2981767324255272,"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."}}