{"id":"W2104170615","doi":"10.1016/j.disc.2007.04.044","title":"The reconstruction conjecture and edge ideals","year":2007,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"Dalhousie University","funders":"","keywords":"Mathematics; Combinatorics; Betti number; Conjecture; Hilbert series and Hilbert polynomial; Vertex (graph theory); Discrete mathematics; Monomial ideal; Algebraic number; Simple graph; Krull dimension; Ideal (ethics); Graph; Pure mathematics; Hilbert space; Algebra over a field; Noetherian; Polynomial ring","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":[0.00216861,0.0005153656,0.001009046,0.001109461,0.002038416,0.003756743,0.001227405,0.002505566,0.009779058],"category_scores_gemma":[0.00750868,0.000529612,0.0007074269,0.001491522,0.007347329,0.01390143,0.003003422,0.004389731,0.0009683768],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009703184,"about_ca_system_score_gemma":0.0005610687,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000913801,"about_ca_topic_score_gemma":0.0006046653,"domain_scores_codex":[0.9989145,0.0003873466,0.00004091615,0.0002437777,0.0002321978,0.0001811816],"domain_scores_gemma":[0.9950976,0.003060185,0.0003318558,0.0007765855,0.0004486909,0.0002851253],"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":[0.0000551156,0.00001439407,0.0002709195,0.00002228288,0.000003567247,0.00003351418,0.00009388891,0.0004077959,0.000135906,0.9942689,0.001409541,0.003284144],"study_design_scores_gemma":[0.00001469088,0.000006374066,0.000135735,0.000008387281,0.000003084491,0.00004548092,0.00008012338,0.001222631,0.0001801815,0.9959314,0.002367289,0.000004488746],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4854136,0.007270951,0.166082,0.04326538,0.001232917,0.00005509791,0.0005510587,0.000483993,0.295645],"genre_scores_gemma":[0.9659407,0.001846599,0.01052663,0.001447401,0.0008764248,0.0000230886,0.0004936986,0.00006860664,0.01877681],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009779058,"threshold_uncertainty_score":0.03271425,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02916167738349223,"score_gpt":0.3266315288298406,"score_spread":0.2974698514463484,"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."}}