{"id":"W4414542636","doi":"10.1007/s00454-025-00771-0","title":"A Stability Theorem for Bigraded Persistence Barcodes","year":2025,"lang":"en","type":"article","venue":"Discrete & Computational Geometry","topic":"Topological and Geometric Data Analysis","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Regina","funders":"Natural Sciences and Engineering Research Council of Canada; National Research Foundation of Korea; Serbian Academy of Sciences and Arts; Simons Foundation","keywords":"Homology (biology); Persistent homology; Filtration (mathematics); Stability (learning theory); Persistence (discontinuity)","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005535773,0.0001778021,0.0002805592,0.0005568231,0.0002925444,0.0002177081,0.001132746,0.00006947063,0.00008448901],"category_scores_gemma":[0.0006226362,0.000142225,0.00028375,0.003584985,0.0001747072,0.00034872,0.0003731338,0.0001166893,0.0000232244],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005628001,"about_ca_system_score_gemma":0.0001063143,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002011834,"about_ca_topic_score_gemma":0.000003185948,"domain_scores_codex":[0.9982114,0.00008511423,0.0003446108,0.000657649,0.0003664917,0.0003346725],"domain_scores_gemma":[0.9977967,0.001284788,0.00009430004,0.0004654942,0.0002564987,0.0001022547],"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":[0.00002794311,0.0001483769,0.005149411,0.0000510188,0.0001538402,0.000002789944,0.0001224182,0.005320374,0.00004773866,0.9520402,0.001061246,0.03587465],"study_design_scores_gemma":[0.0007680384,0.0001542473,0.07753077,0.00002753352,0.00006656036,0.000004094961,0.0003283396,0.3431624,0.0003877942,0.5707606,0.006391754,0.0004177932],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03343524,0.0003670072,0.9603308,0.003296496,0.0001772085,0.0002146094,0.0001279182,0.0001414746,0.001909215],"genre_scores_gemma":[0.914184,0.000006164458,0.08449617,0.0007967473,0.00002977383,0.00003950494,0.0001248728,0.000003762097,0.000319006],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.8807487,"threshold_uncertainty_score":0.5799768,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03165396604230301,"score_gpt":0.2832798486479807,"score_spread":0.2516258826056776,"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."}}