{"id":"W2950209990","doi":"10.48550/arxiv.0810.4867","title":"On Systems of Equations over Free Partially Commutative Groups","year":2008,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"Eusko Jaurlaritza","keywords":"Commutative property; Group (periodic table); Mathematics; Pure mathematics; Algebra over a field; Physics; Quantum mechanics","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":[0.001286462,0.000684596,0.0006817267,0.00102795,0.001270303,0.002652029,0.000532379,0.0008428206,0.006802201],"category_scores_gemma":[0.001653001,0.0003017796,0.0009863931,0.001001185,0.002424281,0.003763268,0.002265002,0.001807688,0.0008708141],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001429913,"about_ca_system_score_gemma":0.0005686173,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001363632,"about_ca_topic_score_gemma":0.001077609,"domain_scores_codex":[0.998915,0.0003228161,0.00009176817,0.0002095682,0.0003348993,0.0001259944],"domain_scores_gemma":[0.9994937,0.0001901817,0.0000580169,0.0000767942,0.0001254524,0.00005583147],"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":[0.00000973351,0.000003885179,0.0001149131,0.00002660388,0.000006046792,0.00004580351,0.0002696428,0.0008412712,0.0007477516,0.9941104,0.0008657448,0.002958185],"study_design_scores_gemma":[0.00001483829,0.00001162942,0.0001718009,0.00001227054,0.000005418021,0.00008418499,0.00007028744,0.004584783,0.0006739708,0.9844385,0.009923638,0.000008739454],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.375564,0.004297061,0.4331867,0.006804078,0.001639845,0.0001656871,0.00119716,0.0004769393,0.1766686],"genre_scores_gemma":[0.8801711,0.001583842,0.06678981,0.0007909152,0.0009782932,0.0001811538,0.001154239,0.0001790202,0.0481716],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006802201,"threshold_uncertainty_score":0.02275562,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1188455811369115,"score_gpt":0.329125597930379,"score_spread":0.2102800167934675,"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."}}