{"id":"W4280647429","doi":"10.1007/s00029-025-01021-0","title":"Homotopy path algebras","year":2025,"lang":"en","type":"article","venue":"Selecta Mathematica","topic":"Homotopy and Cohomology in Algebraic Topology","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Homotopy; Mathematics; Morphism; Resolution (logic); Pure mathematics; Class (philosophy); Path (computing); Symmetry (geometry); Cofibration; Algebra over a field; Homotopy lifting property; n-connected; Geometry; Computer science","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":[0.0006883584,0.000679318,0.0006126621,0.002404544,0.002029533,0.004231925,0.0006772088,0.001207033,0.0288278],"category_scores_gemma":[0.001565764,0.0003892419,0.0005173343,0.001887658,0.002800534,0.006787575,0.001832844,0.003103765,0.004458724],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001515301,"about_ca_system_score_gemma":0.0008810905,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00128257,"about_ca_topic_score_gemma":0.0009596592,"domain_scores_codex":[0.999518,0.0001299914,0.00002222412,0.0001179644,0.0001592489,0.00005242123],"domain_scores_gemma":[0.9994317,0.000162831,0.0000446454,0.0000893579,0.0002015779,0.00006989623],"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":[0.000002156813,0.000003354705,0.0000289348,0.000008337452,0.000002052997,0.000009913147,0.00005176997,0.00003983449,0.00008010891,0.9955466,0.002148411,0.002078489],"study_design_scores_gemma":[0.000003521675,0.000003022936,0.0001003062,0.000006954269,0.000003174503,0.00004664316,0.00004061431,0.0003849773,0.0001542106,0.9746317,0.0246213,0.000003712054],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.04089513,0.008229638,0.1115622,0.009652835,0.001883554,0.0000639709,0.0009556662,0.0006965469,0.8260605],"genre_scores_gemma":[0.6204292,0.007814628,0.03207475,0.00235995,0.002815993,0.0001735479,0.001340504,0.0004032476,0.3325882],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.0288278,"threshold_uncertainty_score":0.09643853,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01861884476362478,"score_gpt":0.308707143035826,"score_spread":0.2900882982722012,"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."}}