{"id":"W2949923012","doi":"10.48550/arxiv.0907.2935","title":"Positive expansiveness versus network dimension in symbolic dynamical systems","year":2009,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Cellular Automata and Applications","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Trent University","funders":"","keywords":"Mathematics; Dynamical systems theory; Counterexample; Symbolic dynamics; Countable set; Topological entropy; Dynamical system (definition); Digraph; Invariant (physics); Discrete mathematics; Dimension (graph theory); Topological conjugacy; Exponent; Function (biology); Cellular automaton; Pure mathematics; Combinatorics; Algorithm; Physics","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":[0.0008010974,0.0003510612,0.0003879786,0.001063839,0.0007462213,0.001871015,0.0003740985,0.0005007746,0.002218069],"category_scores_gemma":[0.004512782,0.0002551631,0.0003595001,0.0005353614,0.00491839,0.003390454,0.002184521,0.0009486497,0.0001133943],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007443338,"about_ca_system_score_gemma":0.0002094455,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000395604,"about_ca_topic_score_gemma":0.0002550174,"domain_scores_codex":[0.9993117,0.000238166,0.00004134065,0.0001465645,0.0001743211,0.00008800039],"domain_scores_gemma":[0.9943269,0.003677215,0.0007354174,0.0005859876,0.000237117,0.0004375048],"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":[0.00003864326,0.00001350746,0.001560362,0.00004313048,0.0000134315,0.000112648,0.0003317202,0.009478595,0.002155707,0.9821786,0.0002119137,0.003861812],"study_design_scores_gemma":[0.00002481725,0.00005518058,0.00173292,0.00002448128,0.00001659234,0.0002129686,0.0001619432,0.06593954,0.001793769,0.9277409,0.002276043,0.0000208254],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8596404,0.0009613461,0.1054614,0.001924879,0.00006588878,0.00003435376,0.0001664044,0.0001123788,0.0316329],"genre_scores_gemma":[0.9965413,0.0002149134,0.002468381,0.00002667413,0.00005378018,0.00002119253,0.00002603697,0.000006058683,0.0006415875],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002218069,"threshold_uncertainty_score":0.007420182,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02761659447878399,"score_gpt":0.2687545962799092,"score_spread":0.2411380018011252,"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."}}