{"id":"W2297068249","doi":"10.4007/annals.2016.184.3.3","title":"On the phase transition in random simplicial complexes","year":2016,"lang":"en","type":"preprint","venue":"Annals of Mathematics","topic":"Topological and Geometric Data Analysis","field":"Computer Science","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Azrieli Foundation","keywords":"Giant component; Combinatorics; Betti number; Mathematics; Random graph; Vertex (graph theory); Phase transition; Order (exchange); Connected component; Graph; Simplicial complex; Discrete mathematics; Physics; Quantum mechanics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009169232,0.0001682812,0.0004989076,0.0002586726,0.00004101705,0.00005998597,0.00125297,0.0001173176,0.00009486593],"category_scores_gemma":[0.0004294586,0.0000855382,0.0002392452,0.0004032018,0.00008639212,0.00006967405,0.0003678142,0.0002019012,0.00003328697],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000006248311,"about_ca_system_score_gemma":0.00003061169,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002384892,"about_ca_topic_score_gemma":0.000004861146,"domain_scores_codex":[0.9985736,0.0001071795,0.000505194,0.0002674896,0.0003544704,0.0001920409],"domain_scores_gemma":[0.9973633,0.001404936,0.0003049302,0.0007959234,0.00009067227,0.00004020132],"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":[0.00005021492,0.00188961,0.00000237284,0.0001958779,0.0001514241,0.00001418676,0.002350722,0.0004661349,0.000182389,0.9659042,0.006624793,0.0221681],"study_design_scores_gemma":[0.0006875899,0.0001168063,0.00003120471,0.0002253053,0.00001890083,0.000001246738,0.00004199033,0.01473739,0.001765131,0.9817396,0.0004776254,0.0001571681],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.115914,0.0001143468,0.8540141,0.02750778,0.00009706504,0.0003440971,0.0002245883,0.00004354426,0.001740444],"genre_scores_gemma":[0.9947668,0.0001486009,0.003621194,0.001306968,0.00006046822,0.00002856581,0.00002005344,0.000006530304,0.00004083408],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8788527,"threshold_uncertainty_score":0.3488147,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.119311658559917,"score_gpt":0.3608076168395019,"score_spread":0.2414959582795849,"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."}}