{"id":"W851324503","doi":"10.1017/cbo9780511808241.009","title":"The Loop Invariant for Lower Bounds","year":2008,"lang":"en","type":"book-chapter","venue":"Cambridge University Press eBooks","topic":"Formal Methods in Verification","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"","keywords":"Loop (graph theory); Invariant (physics); Mathematics; Computer science; Combinatorics; Mathematical 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":[0.001114591,0.0007304341,0.000779723,0.001817472,0.001096159,0.003002263,0.001314834,0.001110623,0.02921501],"category_scores_gemma":[0.005958199,0.0004125682,0.001272041,0.001448671,0.003694445,0.005203828,0.001994488,0.004511429,0.006202138],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002078027,"about_ca_system_score_gemma":0.0008963964,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0014101,"about_ca_topic_score_gemma":0.0007806687,"domain_scores_codex":[0.9985237,0.0001867777,0.00006714339,0.0003222763,0.0006660772,0.0002340745],"domain_scores_gemma":[0.9979004,0.001134917,0.0001254531,0.0004649059,0.0003000513,0.0000742742],"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":[0.00002501756,0.00001080441,0.00005139529,0.00006896918,0.00000443125,0.00003100737,0.0000805231,0.001410087,0.0004719292,0.965638,0.007251009,0.02495677],"study_design_scores_gemma":[0.00000746088,0.00001507361,0.0001007719,0.00005574069,0.000008763517,0.0000438722,0.00001421781,0.004444925,0.001230994,0.9688761,0.02519178,0.00001016274],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"methods","genre_scores_codex":[0.01370769,0.006226832,0.3552268,0.002551629,0.001028936,0.00004947731,0.0005518854,0.001673829,0.6189829],"genre_scores_gemma":[0.7306577,0.007021909,0.08123491,0.002611485,0.002259044,0.0004211273,0.001338953,0.003350457,0.1711044],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.02921501,"threshold_uncertainty_score":0.09773391,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0410786066416894,"score_gpt":0.2296455521685621,"score_spread":0.1885669455268726,"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."}}