{"id":"W2950733771","doi":"10.4153/cmb-2012-043-9","title":"Closure of the Cone of Sums of 2<i>d</i>-powers in Certain Weighted ℓ<sub>1</sub>-seminorm Topologies","year":2012,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Saskatchewan","funders":"","keywords":"Mathematics; Semigroup; Hypercube; Cone (formal languages); Closure (psychology); Norm (philosophy); Commutative property; Discrete mathematics; Combinatorics; Pure mathematics; Topology (electrical circuits)","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0006627481,0.0002164571,0.0006477979,0.0001657051,0.00003733665,0.000004257469,0.0004908567,0.0002246074,0.001127062],"category_scores_gemma":[0.002626042,0.0001646905,0.0001638079,0.0003205174,0.0006031605,0.00003667558,0.0001026533,0.000291538,0.0000721016],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001569408,"about_ca_system_score_gemma":0.0001702697,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003322072,"about_ca_topic_score_gemma":0.001268591,"domain_scores_codex":[0.9979556,0.0001258089,0.0008760021,0.0001692597,0.0003256092,0.0005477326],"domain_scores_gemma":[0.9972509,0.001313638,0.0003804865,0.0007116354,0.000116573,0.0002267837],"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":[0.00001672812,0.0001797447,0.007349968,0.0009273919,0.00005661655,0.000004957554,0.001726508,0.000001554502,0.006597625,0.9786971,0.004082788,0.0003590137],"study_design_scores_gemma":[0.0005966544,0.0000588951,0.002104848,0.0005448958,0.00006876502,0.00001615997,0.001255559,0.00001552005,0.2390185,0.7538384,0.00219136,0.0002905123],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9873692,0.0002059319,0.0002689607,0.001268589,0.0001376424,0.000477644,0.00005084717,0.00001758093,0.01020364],"genre_scores_gemma":[0.993072,0.00001330295,0.006473881,0.00009696263,0.00003330621,0.00002012834,0.000002208503,0.00003422841,0.0002539195],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2324209,"threshold_uncertainty_score":0.999786,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02279515564046755,"score_gpt":0.263401533862138,"score_spread":0.2406063782216705,"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."}}