{"id":"W7155082362","doi":"10.1109/synasc69064.2025.00016","title":"Factorial Powers","year":2025,"lang":"","type":"article","venue":"","topic":"Physics and Engineering Research Articles","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University","funders":"","keywords":"Factorial; Monomial; Stirling numbers of the first kind; Integer (computer science); Stirling numbers of the second kind; Factorial experiment; Stirling number; Stirling engine","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00009921176,0.0001817023,0.0001737393,0.0001399915,0.00006649958,0.0001367883,0.0002154502,0.00007955205,0.0005156662],"category_scores_gemma":[0.0000533004,0.0001874692,0.00009947273,0.0004479731,0.00003775743,0.0001497479,0.00008784878,0.0002444985,0.0003180454],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001253476,"about_ca_system_score_gemma":0.00006424645,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004700965,"about_ca_topic_score_gemma":0.000003748669,"domain_scores_codex":[0.998907,0.0000101484,0.0001977355,0.0001808957,0.0001753113,0.0005288552],"domain_scores_gemma":[0.999438,0.00008458533,0.00000620917,0.0002906852,0.00003953028,0.0001410256],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00006023319,0.0001973594,0.0007240093,0.0006672951,0.0009439241,0.00002104086,0.0004999121,0.1160241,0.1471923,0.3140568,0.1119643,0.3076488],"study_design_scores_gemma":[0.001853878,0.0001111369,0.004806061,0.0002831928,0.000069246,7.431314e-7,0.0001867625,0.5793767,0.07926472,0.1497249,0.1834166,0.000906089],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.3656462,0.001847873,0.1058441,0.0008202118,0.01024556,0.0003440894,0.00002243597,0.0007519645,0.5144775],"genre_scores_gemma":[0.9976879,0.0001891224,0.0002830151,0.00002994393,0.0002534034,0.000006987721,0.000001690537,0.00002082516,0.001527105],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6320417,"threshold_uncertainty_score":0.7644773,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.006478917770895805,"score_gpt":0.2402480414048302,"score_spread":0.2337691236339344,"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."}}