{"id":"W4225358679","doi":"10.48550/arxiv.2111.06391","title":"Persistence of Periodic Orbits under State-dependent Delayed Perturbations: Computer-assisted Proofs","year":2021,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Numerical methods for differential equations","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Ministero dell’Istruzione, dell’Università e della Ricerca; Agencia Estatal de Investigación; National Science Foundation","keywords":"Ode; Mathematics; Ordinary differential equation; Mathematical proof; Perturbation (astronomy); Periodic orbits; Chebyshev polynomials; Polynomial; Differential equation; Mathematical analysis; Applied mathematics; Physics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.000313536,0.0004491346,0.0008071535,0.0002933236,0.0002067683,0.0001040553,0.0007719789,0.0003463236,0.0002755036],"category_scores_gemma":[0.0003125208,0.0004983972,0.0005183168,0.0006451746,0.000254491,0.000175653,0.001046301,0.000718571,0.00001689934],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004377775,"about_ca_system_score_gemma":0.00048783,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001623483,"about_ca_topic_score_gemma":0.0001620516,"domain_scores_codex":[0.997129,0.0006225299,0.0005848293,0.001016187,0.0002679905,0.0003795184],"domain_scores_gemma":[0.996569,0.0007253566,0.0007216151,0.001072781,0.0006972475,0.0002139373],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.001239654,0.01369145,0.008130513,0.00891045,0.01136008,0.001897958,0.02097118,0.5563769,0.01014424,0.3331882,0.0005242055,0.03356513],"study_design_scores_gemma":[0.002466827,0.0005873773,0.009527484,0.001310984,0.002529216,0.00005069298,0.004650854,0.2889374,0.002027091,0.6857333,0.00004431357,0.002134426],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4597062,0.00005328748,0.5390956,0.00004512076,0.0003269239,0.0004073805,0.00006654124,0.0001081578,0.0001907628],"genre_scores_gemma":[0.9157739,0.00007286954,0.08253964,0.00002939967,0.00004319552,0.000005181683,0.00008945502,0.00005442686,0.001391906],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.456556,"threshold_uncertainty_score":0.9997467,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2013113859833409,"score_gpt":0.2622392053572483,"score_spread":0.06092781937390745,"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."}}