{"id":"W2786628285","doi":"10.1007/s40509-018-0176-8","title":"Towards space from Hilbert space: finding lattice structure in finite-dimensional quantum systems","year":2018,"lang":"en","type":"preprint","venue":"Quantum Studies Mathematics and Foundations","topic":"Cosmology and Gravitation Theories","field":"Physics and Astronomy","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada; Walter Burke Institute for Theoretical Physics; Office of Science; Foundational Questions Institute; California Institute of Technology; Simons Foundation; High Energy Physics; U.S. Department of Energy","keywords":"Hilbert space; SIC-POVM; Projective Hilbert space; Tensor product; Mathematics; Theoretical physics; Rigged Hilbert space; Pure mathematics; Quantum mechanics; Physics; Quantum; Reproducing kernel Hilbert space; Quantum dynamics; Quantum operation","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00171401,0.0006410873,0.001074558,0.001960601,0.001522654,0.003840898,0.002354226,0.001947261,0.002762846],"category_scores_gemma":[0.009936996,0.0006590936,0.0006653069,0.001428151,0.006238234,0.007649351,0.003747514,0.00348995,0.0004519835],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009194301,"about_ca_system_score_gemma":0.001178764,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002342863,"about_ca_topic_score_gemma":0.001704987,"domain_scores_codex":[0.9992854,0.000369034,0.000031942,0.0000835879,0.0001682322,0.00006183932],"domain_scores_gemma":[0.9963732,0.002209191,0.0002343446,0.0003731563,0.0003942703,0.0004157955],"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":[0.00003576068,0.00004573214,0.00057272,0.0001026605,0.00001348935,0.00003812953,0.0004492033,0.01132873,0.0008053142,0.9775704,0.001158878,0.007878979],"study_design_scores_gemma":[0.000006931585,0.000005714553,0.00005984036,0.00001118728,0.000001521146,0.0000115142,0.00008764621,0.03721955,0.0001088558,0.9620668,0.0004136817,0.000006775924],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3254092,0.003300698,0.6387661,0.007382233,0.0003083086,0.00008271703,0.000351737,0.000375094,0.02402396],"genre_scores_gemma":[0.8478037,0.001122304,0.1456934,0.0004642221,0.0002532267,0.00008140878,0.0003032287,0.0001108631,0.004167694],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003840898,"threshold_uncertainty_score":0.009242654,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04105911276709297,"score_gpt":0.3244948011692826,"score_spread":0.2834356884021896,"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."}}