{"meta":{"query_hash":"93437ec0504a","filters":{"venue":"Communications in Partial Differential Equations"},"cohort_total":19,"direct_labels_cover":0,"predictions_cover":19,"exported":19,"export_cap":100000,"truncated":false,"label_status":"direct model label, unvalidated","prediction_status":"machine_predicted_unvalidated (Codex and Gemma teacher distillation)","score_status":"score_only:v0-immature-baseline","snapshot":{"source":"OpenAlex, pinned release, all 482 partitions","release":"2026-06-24","frame_built":"2026-07-12"},"permalink":"https://metacan.xera.ac/q/93437ec0504a","api":"https://metacan.xera.ac/api/v1/cohort?venue=Communications+in+Partial+Differential+Equations"},"results":[{"id":"W1511144765","doi":"10.1080/03605302.2019.1611846","title":"On Serrin’s overdetermined problem and a conjecture of Berestycki, Caffarelli and Nirenberg","year":2019,"lang":"en","type":"article","venue":"Communications in Partial Differential Equations","topic":"Advanced Mathematical Modeling in Engineering","field":"Computer Science","cited_by":8,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Epigraph; Counterexample; Overdetermined system; Nirenberg and Matthaei experiment; Mathematics; Conjecture; Pure mathematics; Lipschitz continuity; Rigidity (electromagnetism); Combinatorics; Mathematical analysis; Physics","score_opus":0.025428219923323427,"score_gpt":0.28419203173172164,"score_spread":0.2587638118083982,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1511144765","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"metacan-v3-hybrid-931329e0061c","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.39538676,0.004964956,0.4115815,0.03926712,0.0012551514,0.00011300365,0.0008397321,0.0007229344,0.14586873],"genre_scores_gemma":[0.92144734,0.002168048,0.051648013,0.0023119836,0.0015319844,0.000095106516,0.00050804636,0.00023267047,0.020056695],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99650323,0.0012661644,0.000119446886,0.0009444082,0.0007217206,0.00044499166],"domain_scores_gemma":[0.9863896,0.00804192,0.0014926506,0.00170542,0.0011149804,0.0012555282],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0039756843,0.0010423736,0.0014239325,0.0018047376,0.003328519,0.0022861757,0.0020980332,0.0034533644,0.008946905],"category_scores_gemma":[0.019183883,0.000934767,0.001625493,0.0015565798,0.008611061,0.010413654,0.005032089,0.0060562617,0.00072359416],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0000670679,0.000022540322,0.0004836424,0.000079826386,0.000015670103,0.00014587956,0.00055921345,0.005753343,0.00032689853,0.983925,0.0033851704,0.005235777],"study_design_scores_gemma":[0.000027470063,0.00003636437,0.00068825606,0.000037530048,0.000012902973,0.00018923152,0.00023055151,0.016304843,0.000339722,0.9754666,0.006625152,0.000041291678],"about_ca_topic_score_codex":0.0041009323,"about_ca_topic_score_gemma":0.0022537734,"teacher_disagreement_score":0.008946905,"about_ca_system_score_codex":0.0018994713,"about_ca_system_score_gemma":0.0013638922,"threshold_uncertainty_score":0.029930353},"labels":[],"label_agreement":null},{"id":"W1626051177","doi":"10.1080/03605302.2015.1123272","title":"<i>L</i><sup>2</sup>orbital stability of Dirac solitons in the massive Thirring model","year":2015,"lang":"en","type":"article","venue":"Communications in Partial Differential Equations","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":35,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"McMaster University","funders":"","keywords":"Thirring model; Mathematical physics; Dirac (video compression format); Integrable system; Transformation (genetics); Physics; Stability (learning theory); Inverse; Mathematics; Quantum mechanics; Fermion; Geometry; Chemistry","score_opus":0.24014251931763989,"score_gpt":0.3916811731542902,"score_spread":0.1515386538366503,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1626051177","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"metacan-v3-hybrid-931329e0061c","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.77462536,0.000732919,0.17509866,0.002197364,0.00019704532,0.000037473324,0.000100978345,0.000304044,0.04670608],"genre_scores_gemma":[0.98869205,0.00016363074,0.0061650476,0.00013933126,0.00006754443,0.00002116674,0.00002969132,0.00004417,0.004677343],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99987566,0.00003793373,0.000006460186,0.00001739652,0.000036154113,0.000026496436],"domain_scores_gemma":[0.99954283,0.00012861998,0.000098455115,0.00006006972,0.00008192318,0.0000880624],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00058489206,0.0005819172,0.0003330885,0.000711707,0.00062424416,0.001023803,0.0004746151,0.00064310397,0.0024695576],"category_scores_gemma":[0.0013386569,0.0001515548,0.0004986768,0.00028899082,0.0016409336,0.0011507504,0.0012798931,0.0009606882,0.00034538045],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00007113372,0.000035659323,0.0010484257,0.00007526198,0.000019218942,0.0004683141,0.00029607015,0.02481692,0.01979867,0.94740796,0.00123727,0.0047250125],"study_design_scores_gemma":[0.000021272863,0.00007611773,0.00074176694,0.000019956848,0.000009151412,0.00036165232,0.00016495331,0.41064885,0.004588471,0.5823796,0.00096053217,0.000027616616],"about_ca_topic_score_codex":0.0009834367,"about_ca_topic_score_gemma":0.00044790766,"teacher_disagreement_score":0.0024695576,"about_ca_system_score_codex":0.00052370504,"about_ca_system_score_gemma":0.00042700494,"threshold_uncertainty_score":0.008261561},"labels":[],"label_agreement":null},{"id":"W1978896895","doi":"10.1081/pde-120016157","title":"THE GENERALIZED KORTEWEG–DE VRIES EQUATION ON THE HALF LINE","year":2002,"lang":"en","type":"article","venue":"Communications in Partial Differential Equations","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":177,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Korteweg–de Vries equation; Boundary value problem; Forcing (mathematics); Line (geometry); Half line; Boundary (topology); Work (physics); Initial value problem; Mathematical analysis; Calculus (dental); Applied mathematics; Nonlinear system; Geometry; Physics","score_opus":0.2639447319372959,"score_gpt":0.384281955798471,"score_spread":0.12033722386117512,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1978896895","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"metacan-v3-hybrid-931329e0061c","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.40314683,0.002559739,0.4729387,0.0042959703,0.0005197215,0.00015802988,0.00054973364,0.000218562,0.1156128],"genre_scores_gemma":[0.9322324,0.000988746,0.029959586,0.0004339193,0.00017579256,0.00017298893,0.00024865926,0.00007726907,0.035710614],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9997472,0.0000688751,0.0000124214175,0.00003981869,0.000099496654,0.000032146887],"domain_scores_gemma":[0.9997482,0.000088186905,0.000039998482,0.000030804847,0.000056131124,0.00003668066],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00042977778,0.00054818235,0.00083674426,0.00048478507,0.00049994874,0.001979876,0.0009494577,0.0016723776,0.0053453497],"category_scores_gemma":[0.0011069092,0.00022995925,0.0005071249,0.00041703563,0.0021028516,0.0019727452,0.0013409805,0.0011814327,0.0005322912],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.000091951355,0.00003738896,0.00040384932,0.0001472438,0.000029158318,0.0008999901,0.0002357862,0.09306352,0.0124371275,0.87993264,0.0019550754,0.010766234],"study_design_scores_gemma":[0.000081488244,0.000042223488,0.0005007103,0.00004625201,0.000012151773,0.00033509734,0.00015083581,0.645673,0.0041934955,0.34166032,0.0072597237,0.000044713106],"about_ca_topic_score_codex":0.0021386794,"about_ca_topic_score_gemma":0.00077021756,"teacher_disagreement_score":0.0053453497,"about_ca_system_score_codex":0.00097344455,"about_ca_system_score_gemma":0.0007977635,"threshold_uncertainty_score":0.01788193},"labels":[],"label_agreement":null},{"id":"W1983195501","doi":"10.1081/pde-200037760","title":"Convergence of the Neumann Series in Higher Norms","year":2004,"lang":"en","type":"article","venue":"Communications in Partial Differential Equations","topic":"Nonlinear Waves and Solitons","field":"Physics and Astronomy","cited_by":3,"is_retracted":false,"has_abstract":true,"route_ca_aff":false,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"","funders":"McMaster University","keywords":"Neumann series; Mathematics; Convergence (economics); Series (stratigraphy); Normal convergence; Von Neumann architecture; Applied mathematics; Mathematical economics; Mathematical analysis; Pure mathematics; Rate of convergence; Computer science; Economics; Geology; Key (lock)","score_opus":0.054686522607248156,"score_gpt":0.30980988139036125,"score_spread":0.2551233587831131,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W1983195501","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"metacan-v3-hybrid-931329e0061c","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.38306907,0.0013923094,0.46188557,0.0043809875,0.0010026244,0.00008164095,0.00024356361,0.00041899047,0.1475252],"genre_scores_gemma":[0.9085004,0.0012979722,0.057169866,0.0005978854,0.00090388657,0.00022691429,0.0002966463,0.00039805938,0.030608462],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9968286,0.0012174342,0.00018297258,0.00037846545,0.0010925004,0.00029990778],"domain_scores_gemma":[0.9877671,0.0061233747,0.00077538885,0.0007843972,0.0031374765,0.0014122747],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0053541926,0.0010849977,0.00092339213,0.0038766798,0.0015761212,0.003943069,0.0013344282,0.0011848864,0.006825991],"category_scores_gemma":[0.018835662,0.00044527464,0.0010816704,0.0012429613,0.005382104,0.008522384,0.0041543576,0.0035681229,0.0010398226],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.000023035449,0.000017869983,0.00012538301,0.000022303315,0.0000055391733,0.000054500757,0.00017686796,0.0013614967,0.0010634935,0.9950932,0.00033030653,0.0017259519],"study_design_scores_gemma":[0.000009488084,0.000028153096,0.00019269613,0.000017191122,0.0000037099005,0.00010416026,0.00008554559,0.027892342,0.00096202904,0.96929026,0.0013991521,0.000015294303],"about_ca_topic_score_codex":0.00067134463,"about_ca_topic_score_gemma":0.0005598827,"teacher_disagreement_score":0.006825991,"about_ca_system_score_codex":0.0019050281,"about_ca_system_score_gemma":0.00088652474,"threshold_uncertainty_score":0.028316021},"labels":[],"label_agreement":null},{"id":"W2070601934","doi":"10.1080/03605300802031614","title":"The Cauchy Problem for Defocusing Nonlinear Schrödinger Equations with Non-Vanishing Initial Data at Infinity","year":2008,"lang":"en","type":"article","venue":"Communications in Partial Differential Equations","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":69,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"McMaster University","funders":"","keywords":"Infinity; Initial value problem; Domain (mathematical analysis); Nonlinear system; Mathematics; Cauchy distribution; Mathematical analysis; Mathematical physics; Cauchy problem; Physics; Quantum mechanics","score_opus":0.2912508676815113,"score_gpt":0.41939578265182254,"score_spread":0.12814491497031122,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2070601934","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"metacan-v3-hybrid-931329e0061c","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.49226812,0.0010744758,0.4726052,0.002599443,0.00015417238,0.00011693712,0.00015897518,0.00007991304,0.030942813],"genre_scores_gemma":[0.8878947,0.0012657848,0.0795994,0.00032005427,0.00020644855,0.00016991083,0.00039613235,0.000091153546,0.030056484],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99971753,0.000100403406,0.00001911037,0.000047292753,0.000078484874,0.000037151498],"domain_scores_gemma":[0.9986852,0.0006649175,0.0001822822,0.00007372878,0.00022276056,0.00017117852],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0014638208,0.001106135,0.00061425264,0.0011157038,0.0009122603,0.0015123197,0.00082222454,0.0017578822,0.00188451],"category_scores_gemma":[0.004707939,0.00036920613,0.0006168228,0.0003067407,0.0025132021,0.0031471432,0.0028386076,0.0019618548,0.00027487235],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00015437129,0.000070394075,0.0014591694,0.00029319478,0.000039601986,0.0009212245,0.00087404135,0.06435848,0.022990296,0.89801127,0.0011907021,0.009637244],"study_design_scores_gemma":[0.000057882837,0.00016141712,0.0011224226,0.000058040154,0.000017933318,0.00056270947,0.00041111422,0.5238424,0.009203114,0.4618968,0.0026053376,0.00006093959],"about_ca_topic_score_codex":0.0014162678,"about_ca_topic_score_gemma":0.0008078657,"teacher_disagreement_score":0.00188451,"about_ca_system_score_codex":0.0008072527,"about_ca_system_score_gemma":0.0010157779,"threshold_uncertainty_score":0.007741511},"labels":[],"label_agreement":null},{"id":"W2083017538","doi":"10.1080/03605302.2014.963604","title":"Hydrodynamic Limit of the Gross-Pitaevskii Equation","year":2014,"lang":"en","type":"article","venue":"Communications in Partial Differential Equations","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Vortex; Mathematics; Gross–Pitaevskii equation; Infinity; Ode; Euler equations; Euler's formula; Mathematical physics; Limit (mathematics); Mathematical analysis; Compressibility; Bose–Einstein condensate; Physics; Quantum mechanics; Mechanics","score_opus":0.11498813699002473,"score_gpt":0.3617966954337207,"score_spread":0.24680855844369598,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2083017538","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"metacan-v3-hybrid-931329e0061c","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.71956307,0.0028738235,0.18196337,0.006438763,0.00069915206,0.00013159512,0.0004370307,0.00059699477,0.087296225],"genre_scores_gemma":[0.9619255,0.0006867536,0.014456256,0.0005405433,0.00026266935,0.00015649396,0.00026003955,0.00010494891,0.021606712],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9997335,0.00007204903,0.000011193316,0.000049917755,0.00007550558,0.000057754605],"domain_scores_gemma":[0.9992781,0.0001584563,0.00014884952,0.000047224654,0.00014845075,0.00021882738],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005422584,0.0007319783,0.00085245096,0.0011419795,0.00095821236,0.0018246043,0.0009309102,0.0015392335,0.0027592725],"category_scores_gemma":[0.0034352085,0.0004058455,0.00056231633,0.00041990858,0.0027921386,0.0029790294,0.002691608,0.0014656989,0.00041087813],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.000106848915,0.00008182849,0.00125515,0.00012267662,0.000050318253,0.0006292341,0.0003849194,0.059939373,0.009067922,0.9229649,0.0026358922,0.0027609244],"study_design_scores_gemma":[0.000098967066,0.00009677449,0.001307983,0.000050912116,0.000025996722,0.00030815118,0.0001404595,0.68808734,0.0013990477,0.3059198,0.0025155996,0.000048913826],"about_ca_topic_score_codex":0.0038876995,"about_ca_topic_score_gemma":0.0012814886,"teacher_disagreement_score":0.0038876995,"about_ca_system_score_codex":0.0011917243,"about_ca_system_score_gemma":0.0012342628,"threshold_uncertainty_score":0.009230733},"labels":[],"label_agreement":null},{"id":"W2124749764","doi":"10.1080/03605302.2014.1003073","title":"Symmetry Results for Fractional Elliptic Systems and Related Problems","year":2015,"lang":"en","type":"article","venue":"Communications in Partial Differential Equations","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Monotonic function; Monotone polygon; Fractional Laplacian; Hamiltonian (control theory); Hamiltonian system; Symmetry (geometry); Laplace operator; Pure mathematics; Elliptic operator; p-Laplacian; Mathematical physics; Combinatorics; Mathematical analysis; Geometry; Boundary value problem","score_opus":0.21079282295140703,"score_gpt":0.3915548931449809,"score_spread":0.18076207019357385,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2124749764","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"metacan-v3-hybrid-931329e0061c","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.4537727,0.0026945346,0.46277002,0.004369073,0.00037944978,0.00013973642,0.00019605043,0.00011883515,0.07555971],"genre_scores_gemma":[0.96357,0.0010348549,0.019853426,0.00030103675,0.00023613125,0.000095054005,0.00010941744,0.00006397363,0.014736089],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9996586,0.00011526415,0.000017607768,0.00004116244,0.00010459798,0.00006277282],"domain_scores_gemma":[0.99944955,0.00016574083,0.00015275301,0.000054274948,0.00008323107,0.00009440413],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00090485794,0.00059657724,0.0005877259,0.0008849571,0.000851667,0.0009080275,0.00072480296,0.00094455335,0.0033007495],"category_scores_gemma":[0.0016753529,0.00024970324,0.00088658766,0.00036613864,0.0016423505,0.0018612852,0.0019452659,0.0010113164,0.00030870896],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.000022455884,0.000031496915,0.0004200654,0.000064509986,0.00002069775,0.00022394944,0.00018878875,0.020774808,0.0035783078,0.9692672,0.00088930567,0.004518438],"study_design_scores_gemma":[0.000029374949,0.000055072618,0.00050332193,0.000019716366,0.000009979103,0.00020790791,0.00018631946,0.23675342,0.001268832,0.7587856,0.0021613766,0.000019096586],"about_ca_topic_score_codex":0.0010471311,"about_ca_topic_score_gemma":0.0004689676,"teacher_disagreement_score":0.0033007495,"about_ca_system_score_codex":0.0008744994,"about_ca_system_score_gemma":0.0005473655,"threshold_uncertainty_score":0.011042118},"labels":[],"label_agreement":null},{"id":"W2149671842","doi":"10.1081/pde-120019375","title":"Sharp Spectral Asymptotics for Operators with Irregular Coefficients. I. Pushing the Limits","year":2003,"lang":"en","type":"article","venue":"Communications in Partial Differential Equations","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":20,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Remainder; Mathematics; Semiclassical physics; Modulus of continuity; Hamiltonian (control theory); Mathematical analysis; Spectral properties; Pure mathematics; Type (biology); Quantum; Quantum mechanics","score_opus":0.11902182151507688,"score_gpt":0.36889782180340186,"score_spread":0.24987600028832496,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2149671842","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"metacan-v3-hybrid-931329e0061c","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.70311457,0.0012847183,0.2478668,0.0016593905,0.0002231833,0.0000583616,0.00010106575,0.0006649876,0.04502693],"genre_scores_gemma":[0.97992504,0.0003904645,0.014806206,0.0002000767,0.0001411178,0.000034658537,0.000048717262,0.00010325766,0.0043504476],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9994636,0.0001337644,0.000037506124,0.000068080306,0.00021429418,0.000082625644],"domain_scores_gemma":[0.9976398,0.0008662284,0.00035646462,0.00036470185,0.00039719083,0.0003757],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0015457511,0.0006712605,0.000596908,0.0018763202,0.00069106685,0.0015768921,0.00093464286,0.0009380369,0.0031417771],"category_scores_gemma":[0.008760646,0.00031071712,0.0006395814,0.00042057503,0.0032315413,0.003696223,0.002614123,0.0018175321,0.00036211265],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00007508467,0.000044014734,0.00095515914,0.00011151143,0.000012372164,0.00047734665,0.00044179294,0.0070684175,0.010806967,0.9726582,0.0007442647,0.006604752],"study_design_scores_gemma":[0.00002665184,0.00008012303,0.0016992055,0.000070109774,0.000016182526,0.00068908883,0.00028124527,0.19411567,0.0052610254,0.7954586,0.0022589634,0.000043130527],"about_ca_topic_score_codex":0.00065357226,"about_ca_topic_score_gemma":0.0003829627,"teacher_disagreement_score":0.0031417771,"about_ca_system_score_codex":0.00090182124,"about_ca_system_score_gemma":0.0003269098,"threshold_uncertainty_score":0.010510325},"labels":[],"label_agreement":null},{"id":"W2150486569","doi":"10.1080/03605302.2015.1081609","title":"Singular Ricci Solitons and Their Stability under the Ricci Flow","year":2015,"lang":"en","type":"article","venue":"Communications in Partial Differential Equations","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; Alfred P. Sloan Foundation","keywords":"Mathematics; Ricci flow; Singularity; Flow (mathematics); Mathematical analysis; Singular point of a curve; Stability (learning theory); Sobolev space; Curvature; Metric (unit); Ricci curvature; Pure mathematics; Mathematical physics; Geometry","score_opus":0.20304360706441407,"score_gpt":0.357126160693978,"score_spread":0.15408255362956394,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2150486569","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"metacan-v3-hybrid-931329e0061c","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.8772692,0.0005000323,0.10807472,0.0005832661,0.00006886321,0.000052088268,0.00007289064,0.00018786869,0.013191127],"genre_scores_gemma":[0.991102,0.0001626378,0.0051018153,0.000048748647,0.000029114728,0.000022621029,0.000049200382,0.000022951635,0.0034609744],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99988115,0.000022216258,0.0000065718377,0.000023144035,0.000034631496,0.000032289743],"domain_scores_gemma":[0.99965084,0.000046809808,0.00010485614,0.00002896161,0.00007866705,0.00008989707],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003437852,0.00051873864,0.00034286256,0.001013069,0.0006919308,0.0008992507,0.00040764772,0.0006101784,0.0011578172],"category_scores_gemma":[0.0012229099,0.0001987845,0.0004996508,0.00024436836,0.0016568168,0.0008076106,0.0010894259,0.0005888074,0.00016355561],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00014260928,0.000054807693,0.0027281502,0.00008763392,0.00005757217,0.0012144084,0.0010159408,0.10581345,0.08820919,0.7908298,0.0009955504,0.008850911],"study_design_scores_gemma":[0.000037886475,0.00016262736,0.002800485,0.000022271162,0.000024324932,0.00062511617,0.00047302782,0.68619263,0.01259699,0.2947646,0.0022312237,0.00006877176],"about_ca_topic_score_codex":0.002029698,"about_ca_topic_score_gemma":0.0006122753,"teacher_disagreement_score":0.002029698,"about_ca_system_score_codex":0.0008600795,"about_ca_system_score_gemma":0.00041705804,"threshold_uncertainty_score":0.006240368},"labels":[],"label_agreement":null},{"id":"W2535071976","doi":"10.1080/03605302.2017.1323922","title":"Rotationally corrected scaling invariant solutions to the Navier–Stokes equations","year":2017,"lang":"en","type":"article","venue":"Communications in Partial Differential Equations","topic":"Navier-Stokes equation solutions","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Scaling; Invariant (physics); Navier–Stokes equations; Mathematical analysis; Space (punctuation); Mathematical physics; Compressibility; Geometry; Physics; Mechanics","score_opus":0.25127936664756156,"score_gpt":0.4144225368176618,"score_spread":0.16314317017010022,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2535071976","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"metacan-v3-hybrid-931329e0061c","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.48131466,0.0004655978,0.4687139,0.0012063842,0.0007641606,0.00010873228,0.0001987031,0.0003985942,0.04682931],"genre_scores_gemma":[0.886771,0.00054016046,0.078615636,0.0004533132,0.00029510356,0.00010769037,0.00024593418,0.00020882356,0.03276224],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9998223,0.000033585602,0.000011440492,0.000029587623,0.00007186801,0.000031258864],"domain_scores_gemma":[0.9996117,0.00005012843,0.000089375615,0.00006903323,0.00010323985,0.00007664814],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00034485335,0.0005159471,0.00041453302,0.00066686026,0.0006022649,0.0011099486,0.00070826133,0.0007008621,0.0034025786],"category_scores_gemma":[0.0014132129,0.00019951671,0.000563045,0.00024182786,0.0011503346,0.0014391526,0.001275919,0.0013634488,0.0004457754],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.000028825165,0.000041747782,0.00037151139,0.000039837305,0.000008756455,0.00015622929,0.00016555529,0.008748896,0.019152077,0.95971906,0.0013763382,0.010191146],"study_design_scores_gemma":[0.00006991566,0.00013576829,0.0012977798,0.00003687773,0.000015300073,0.0006265864,0.00024786178,0.27732858,0.015976692,0.6935406,0.010647977,0.0000761146],"about_ca_topic_score_codex":0.00053504313,"about_ca_topic_score_gemma":0.00043704413,"teacher_disagreement_score":0.0034025786,"about_ca_system_score_codex":0.00045552038,"about_ca_system_score_gemma":0.0004362163,"threshold_uncertainty_score":0.011382818},"labels":[],"label_agreement":null},{"id":"W2954160816","doi":"10.1080/03605302.2020.1761386","title":"Global existence, regularity, and uniqueness of infinite energy solutions to the Navier-Stokes equations","year":2020,"lang":"en","type":"preprint","venue":"Communications in Partial Differential Equations","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Uniqueness; Small data; Mathematics; Space (punctuation); Mathematical analysis; Energy (signal processing); Lorentz transformation; Class (philosophy); Lorentz space; Navier–Stokes equations; Standard probability space; Physics; Classical mechanics; Compressibility; Computer science; Statistics; Mechanics","score_opus":0.2140409665895484,"score_gpt":0.39727874274403885,"score_spread":0.18323777615449044,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2954160816","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"metacan-v3-hybrid-931329e0061c","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.7493656,0.0008568463,0.2380336,0.0008577816,0.000055067576,0.000033031643,0.00007858347,0.00008670602,0.010632825],"genre_scores_gemma":[0.9814782,0.0003805868,0.013395725,0.00005938466,0.0000587287,0.000042826596,0.00007769033,0.000031906224,0.0044749016],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9997485,0.00009353456,0.000015692372,0.000054760796,0.000055571774,0.0000318456],"domain_scores_gemma":[0.9987451,0.00059098727,0.00022687958,0.000102012404,0.00022156982,0.00011338717],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0010479764,0.0005255826,0.00048440605,0.000915948,0.0005255082,0.0009925847,0.0006454542,0.0005740698,0.0006119279],"category_scores_gemma":[0.0057499274,0.00024649358,0.00045800218,0.00023880547,0.0023608946,0.0018947761,0.0019341718,0.0009286794,0.000107371685],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00018029854,0.0000819129,0.0067071533,0.0003555812,0.000078137986,0.00091069983,0.0009288846,0.083734825,0.0661953,0.82007647,0.0010700225,0.019680684],"study_design_scores_gemma":[0.000031579235,0.00017534361,0.0055023823,0.0000641834,0.000032721888,0.00055941433,0.0007176055,0.4198616,0.020904263,0.549782,0.0023086916,0.000060179424],"about_ca_topic_score_codex":0.0005666237,"about_ca_topic_score_gemma":0.00039124282,"teacher_disagreement_score":0.0010479764,"about_ca_system_score_codex":0.00046471602,"about_ca_system_score_gemma":0.00040595635,"threshold_uncertainty_score":0.005542338},"labels":[],"label_agreement":null},{"id":"W2962984324","doi":"10.1080/03605302.2016.1227337","title":"Global existence for the derivative nonlinear Schrödinger equation by the method of inverse scattering","year":2016,"lang":"en","type":"article","venue":"Communications in Partial Differential Equations","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":55,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; Simons Foundation","keywords":"Sobolev space; Mathematics; Inverse scattering problem; Lipschitz continuity; Nonlinear Schrödinger equation; Mathematical analysis; Nonlinear system; Inverse scattering transform; Inverse; Dispersive partial differential equation; Eigenvalues and eigenvectors; Scattering; Derivative (finance); Quantum inverse scattering method; Equivalence (formal languages); Work (physics); Inverse problem; Real line; Schrödinger equation; Pure mathematics; Physics; Partial differential equation; Quantum mechanics; Geometry","score_opus":0.19743232970251748,"score_gpt":0.42674298991514165,"score_spread":0.22931066021262417,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2962984324","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"metacan-v3-hybrid-931329e0061c","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.03856829,0.00055073376,0.9444062,0.0007709528,0.00012512396,0.000051024876,0.000053276923,0.000088843786,0.015385575],"genre_scores_gemma":[0.61566865,0.0019853716,0.34422788,0.0005166377,0.00037679324,0.00040452246,0.00020978344,0.00025971537,0.03635058],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9997651,0.00008274908,0.00001256092,0.000032641008,0.00008341542,0.000023573479],"domain_scores_gemma":[0.99953866,0.00019208358,0.000042150557,0.000051002182,0.0001128948,0.00006327681],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0010381769,0.0007564083,0.00062222814,0.0011190568,0.0005264538,0.000779271,0.00065856276,0.0007635648,0.0019012025],"category_scores_gemma":[0.0017157063,0.00033144228,0.0011032872,0.0003356716,0.0018871004,0.0016904725,0.0027231923,0.0018585648,0.00042730646],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.000019839925,0.000024073415,0.0003423123,0.000089882255,0.000022543154,0.00015181559,0.00029079305,0.018788135,0.009858139,0.9602682,0.0010506943,0.009093707],"study_design_scores_gemma":[0.00003270342,0.000081912265,0.00028512042,0.000041977604,0.00002045037,0.00021608725,0.00010186681,0.4552943,0.003062128,0.53374785,0.0070753866,0.0000401695],"about_ca_topic_score_codex":0.0006904079,"about_ca_topic_score_gemma":0.00078896293,"teacher_disagreement_score":0.0019012025,"about_ca_system_score_codex":0.0007116917,"about_ca_system_score_gemma":0.00085291,"threshold_uncertainty_score":0.006360173},"labels":[],"label_agreement":null},{"id":"W2963749589","doi":"10.1080/03605300008821563","title":"Global existence for wave maps with torsion","year":2000,"lang":"en","type":"article","venue":"Communications in Partial Differential Equations","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Brock University","funders":"University of Oregon; National Science Foundation","keywords":"Equivariant map; Mathematics; Lie group; Torsion (gastropod); Invariant (physics); Pure mathematics; Nonlinear system; Sigma; Mathematical analysis; Mathematical physics; Physics; Quantum mechanics","score_opus":0.15048617017661675,"score_gpt":0.3855471064883459,"score_spread":0.23506093631172914,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2963749589","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"metacan-v3-hybrid-931329e0061c","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.7999712,0.00079238426,0.16284426,0.0011972447,0.00013643662,0.000058916008,0.00015016634,0.00022936665,0.034619994],"genre_scores_gemma":[0.97586524,0.0005045064,0.010559515,0.0000714082,0.00014817713,0.00007815599,0.0001794531,0.000088035275,0.012505471],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9997546,0.000062967425,0.000012808429,0.00004007709,0.000061970866,0.00006760652],"domain_scores_gemma":[0.9993481,0.00020136447,0.00012648987,0.000060729817,0.00012149212,0.00014176531],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006341294,0.0010182942,0.00062711333,0.0019155436,0.0010060238,0.0017892699,0.00051175104,0.00089085504,0.0038373799],"category_scores_gemma":[0.0018418438,0.00043310394,0.0007840923,0.0005869796,0.0020619163,0.0032369215,0.0025061022,0.0016222285,0.00039374668],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00003313241,0.000018729455,0.0005230678,0.00004526168,0.000016000136,0.00021909768,0.00026941148,0.004874459,0.0030757652,0.98717415,0.00047046415,0.0032805363],"study_design_scores_gemma":[0.000019348676,0.000060661474,0.0004094318,0.00001976321,0.000019866993,0.00018054334,0.00028642145,0.051983383,0.0019865972,0.9435285,0.0014866501,0.000018836781],"about_ca_topic_score_codex":0.00036314427,"about_ca_topic_score_gemma":0.00037596797,"teacher_disagreement_score":0.0038373799,"about_ca_system_score_codex":0.0007182813,"about_ca_system_score_gemma":0.00055811356,"threshold_uncertainty_score":0.012837291},"labels":[],"label_agreement":null},{"id":"W2963853938","doi":"10.1080/03605302.2012.756520","title":"Stability and Unconditional Uniqueness of Solutions for Energy Critical Wave Equations in High Dimensions","year":2013,"lang":"en","type":"article","venue":"Communications in Partial Differential Equations","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":45,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia","funders":"Leibniz-Gemeinschaft","keywords":"Uniqueness; Mathematics; Wave equation; Nonlinear system; Stability (learning theory); Energy (signal processing); Space (punctuation); Mathematical analysis; Applied mathematics; Physics; Computer science; Quantum mechanics","score_opus":0.17841120965826865,"score_gpt":0.3749767223932327,"score_spread":0.19656551273496406,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W2963853938","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"metacan-v3-hybrid-931329e0061c","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.43572244,0.001962395,0.53396064,0.0013389022,0.00014630888,0.00008055477,0.00015177256,0.00013397445,0.026503032],"genre_scores_gemma":[0.96201694,0.0007569359,0.029365106,0.00026533677,0.00014652617,0.00014014091,0.0001283518,0.000048743383,0.0071318797],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99959964,0.00009985666,0.000030761694,0.000091593516,0.00010807546,0.00007016513],"domain_scores_gemma":[0.99852103,0.0004842511,0.0003067731,0.00010114229,0.00038353694,0.00020327963],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0010824832,0.00066631136,0.000642458,0.0015146219,0.0010004777,0.0011707352,0.00083204656,0.00068881153,0.00217178],"category_scores_gemma":[0.0028779511,0.00030734256,0.00094254233,0.00035433462,0.0022535846,0.002471533,0.0034886538,0.0016700418,0.00029042293],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00006181114,0.00004153882,0.0023513655,0.00019537775,0.000043058633,0.00040081723,0.0005126971,0.024616042,0.02330673,0.9399009,0.00095604634,0.0076136175],"study_design_scores_gemma":[0.00003069443,0.00015143627,0.002933535,0.00006511702,0.000030918625,0.0005140657,0.00042848242,0.35394624,0.010658009,0.6274643,0.0037027556,0.00007433606],"about_ca_topic_score_codex":0.00067983416,"about_ca_topic_score_gemma":0.00046651153,"teacher_disagreement_score":0.00217178,"about_ca_system_score_codex":0.0008223511,"about_ca_system_score_gemma":0.0005923392,"threshold_uncertainty_score":0.0072653294},"labels":[],"label_agreement":null},{"id":"W4240287700","doi":"10.1080/03605300008821515","title":"Asymmetric fermi surfaces for magnetic schrödinger operators","year":2000,"lang":"en","type":"article","venue":"Communications in Partial Differential Equations","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Fermi Gamma-ray Space Telescope; Magnetic field; Fermi surface; Mathematics; Schrödinger's cat; Regular polygon; Magnetic flux; Invariant (physics); Physics; Condensed matter physics; Lattice (music); Mathematical analysis; Quantum mechanics; Mathematical physics; Geometry; Superconductivity","score_opus":0.11093256270187442,"score_gpt":0.38257708872183543,"score_spread":0.27164452601996103,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4240287700","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"metacan-v3-hybrid-931329e0061c","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.88780946,0.0003001991,0.06014245,0.0011461583,0.00009503499,0.00004070032,0.00010326758,0.00012458515,0.05023809],"genre_scores_gemma":[0.98878175,0.00018097322,0.006329044,0.000059761216,0.00006124689,0.000034388122,0.000093026436,0.00003903394,0.0044207787],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9997445,0.00005750506,0.000012039148,0.000028875238,0.00008850708,0.0000685293],"domain_scores_gemma":[0.9995055,0.0002193304,0.00007361924,0.0000470016,0.00006127277,0.00009321231],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004439519,0.0006344223,0.0004497838,0.0015896895,0.0010773239,0.0022736478,0.0005466244,0.0010916933,0.0036798164],"category_scores_gemma":[0.0015750455,0.0002469471,0.0004415645,0.0005262147,0.0017723013,0.0016763452,0.00091831916,0.0008392408,0.00043548297],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.000043582055,0.000020664442,0.00019453061,0.000024309682,0.000003691954,0.00018381464,0.0001319407,0.005100035,0.00507424,0.9868803,0.00034792666,0.0019949903],"study_design_scores_gemma":[0.000034979526,0.00002358496,0.00036660902,0.000012591969,0.0000050629255,0.00021281194,0.00015993221,0.09833667,0.0024985154,0.8972566,0.0010753721,0.00001728286],"about_ca_topic_score_codex":0.00064495706,"about_ca_topic_score_gemma":0.00036429963,"teacher_disagreement_score":0.0036798164,"about_ca_system_score_codex":0.0008637132,"about_ca_system_score_gemma":0.00040096504,"threshold_uncertainty_score":0.012310207},"labels":[],"label_agreement":null},{"id":"W4376609322","doi":"10.1080/03605302.2023.2183408","title":"Maximal speed of quantum propagation for the Hartree equation","year":2023,"lang":"en","type":"article","venue":"Communications in Partial Differential Equations","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Hartree; Mathematics; Speed of light (cellular automaton); Context (archaeology); Lattice (music); Constructive; Nonlinear system; Space (punctuation); Quantum; Light cone; Geodetic datum; State (computer science); Mathematical analysis; Quantum mechanics; Mathematical physics; Physics; Computer science; Algorithm","score_opus":0.2666756564928029,"score_gpt":0.4109033056301529,"score_spread":0.14422764913735003,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4376609322","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"metacan-v3-hybrid-931329e0061c","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.3993217,0.0016379493,0.5730168,0.0019699275,0.00018564041,0.00009389845,0.00022092089,0.00043956572,0.023113593],"genre_scores_gemma":[0.9608749,0.0009981844,0.03176518,0.00024787677,0.00021553496,0.00011514113,0.0001625338,0.00018001167,0.005440547],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9991691,0.00027952882,0.000035794907,0.00011296753,0.0002245668,0.00017805505],"domain_scores_gemma":[0.9912793,0.005343604,0.00092532067,0.00044416133,0.0010956032,0.0009120929],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0029586905,0.0013174126,0.0007970557,0.0021235128,0.001054589,0.0018836618,0.0012996905,0.0009644121,0.002224557],"category_scores_gemma":[0.011446119,0.0005376988,0.0011474037,0.0005401408,0.0032820203,0.004782672,0.0034779515,0.0032453432,0.00027512983],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00012482169,0.000040458643,0.001075266,0.00011508647,0.000037495858,0.00017846697,0.00033064725,0.025437595,0.009621853,0.95766217,0.00081327435,0.004562932],"study_design_scores_gemma":[0.000028428454,0.0001041541,0.0011140449,0.000052075437,0.000032097254,0.00018260551,0.00011894818,0.3663142,0.0048499852,0.6258095,0.0013278495,0.00006601145],"about_ca_topic_score_codex":0.0014030354,"about_ca_topic_score_gemma":0.0005935715,"teacher_disagreement_score":0.0029586905,"about_ca_system_score_codex":0.0018800836,"about_ca_system_score_gemma":0.0011596362,"threshold_uncertainty_score":0.015647233},"labels":[],"label_agreement":null},{"id":"W4407860393","doi":"10.1080/03605302.2025.2459194","title":"A PDE framework of consensus-based optimization for objectives with multiple global minimizers","year":2025,"lang":"en","type":"article","venue":"Communications in Partial Differential Equations","topic":"Advanced Control Systems Optimization","field":"Engineering","cited_by":3,"is_retracted":false,"has_abstract":false,"route_ca_aff":true,"route_ca_fund":false,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"Kootenay Association for Science & Technology","funders":"Munich Center for Machine Learning; Deutsche Forschungsgemeinschaft","keywords":"Mathematics; Applied mathematics; Mathematical optimization; Mathematical economics; Calculus (dental); Medicine","score_opus":0.017921680738133883,"score_gpt":0.2978797935745521,"score_spread":0.2799581128364182,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4407860393","genre_codex":"methods","genre_gemma":"methods","domain_codex":null,"domain_gemma":null,"model_version":"metacan-v3-hybrid-931329e0061c","genre_candidate":"methods","genre_consensus":"methods","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.0010692272,0.00018953824,0.99449664,0.0002620184,0.00007501771,0.000023364806,0.000036788617,0.000028636689,0.0038187406],"genre_scores_gemma":[0.3658842,0.002205676,0.60128456,0.0006767293,0.00070496835,0.00075923704,0.00045755002,0.0003166515,0.027710402],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99913687,0.0003385368,0.000040668318,0.00017871821,0.0002543254,0.000050948387],"domain_scores_gemma":[0.9990589,0.0004479986,0.00009532449,0.0000859008,0.00024326946,0.00006855484],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0018453512,0.0011629576,0.0013669546,0.0009394814,0.00073509174,0.0016549219,0.0021856313,0.0018304618,0.0030819029],"category_scores_gemma":[0.0038694513,0.0006769919,0.0015639113,0.0010256623,0.0016602862,0.0021519288,0.002925577,0.0025682503,0.0005484262],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.0000145905615,0.000031842286,0.00014393612,0.00010585821,0.000040686067,0.00008464628,0.00009511329,0.46597832,0.0017293573,0.517462,0.0024541507,0.011859549],"study_design_scores_gemma":[0.0000065774902,0.000019987658,0.00003974899,0.000010914243,0.0000074159007,0.000018946452,0.00001261492,0.9193403,0.00018634197,0.07813627,0.0022128373,0.000008024101],"about_ca_topic_score_codex":0.003951742,"about_ca_topic_score_gemma":0.0026900712,"teacher_disagreement_score":0.003951742,"about_ca_system_score_codex":0.0012874932,"about_ca_system_score_gemma":0.001895036,"threshold_uncertainty_score":0.010309935},"labels":[],"label_agreement":null},{"id":"W4407931489","doi":"10.1080/03605302.2025.2459197","title":"<i>A priori</i> <i>L</i> <sup>∞</sup> −bound for Ginzburg-Landau energy minimizers with divergence penalization","year":2025,"lang":"en","type":"article","venue":"Communications in Partial Differential Equations","topic":"Advanced Mathematical Modeling in Engineering","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"McMaster University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Divergence (linguistics); A priori and a posteriori; Mathematics; Mathematical physics; Energy (signal processing); Upper and lower bounds; Ginzburg–Landau theory; Combinatorics; Mathematical analysis; Physics; Condensed matter physics; Philosophy; Statistics; Superconductivity","score_opus":0.033341966159133145,"score_gpt":0.29671786006923523,"score_spread":0.2633758939101021,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4407931489","genre_codex":"methods","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"metacan-v3-hybrid-931329e0061c","genre_candidate":"empirical","genre_consensus":null,"domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.39498863,0.0042813653,0.5167648,0.0065466696,0.00028787274,0.00012611455,0.0004591975,0.00053570146,0.07600963],"genre_scores_gemma":[0.9291887,0.0012920162,0.04943105,0.00073260727,0.00017751158,0.00026557856,0.00054178544,0.0005779031,0.017792756],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.99968755,0.00010905596,0.000016226906,0.000065240514,0.000055820194,0.000066238834],"domain_scores_gemma":[0.9976763,0.0011636106,0.00035703628,0.00012799045,0.00029659705,0.0003784865],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0022648522,0.0015140178,0.0007846895,0.0012435563,0.0009337536,0.0022392268,0.0012569898,0.0014518525,0.0040200907],"category_scores_gemma":[0.00847002,0.00045649536,0.0005790805,0.00031621644,0.0025578314,0.0023372965,0.002700511,0.0017967888,0.0004918044],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.00024833856,0.00015669418,0.0038716188,0.0007027993,0.00009526915,0.0004539323,0.00040985673,0.08269943,0.01893429,0.8756918,0.0058271727,0.010908853],"study_design_scores_gemma":[0.000024706449,0.00013283698,0.0024887738,0.0002506501,0.000041231466,0.00033135485,0.0003112623,0.6598612,0.00843443,0.32426295,0.0037945108,0.000066157874],"about_ca_topic_score_codex":0.0012962334,"about_ca_topic_score_gemma":0.0011412242,"teacher_disagreement_score":0.0040200907,"about_ca_system_score_codex":0.0015525905,"about_ca_system_score_gemma":0.0007981441,"threshold_uncertainty_score":0.013448536},"labels":[],"label_agreement":null},{"id":"W4410098334","doi":"10.1080/03605302.2025.2486764","title":"Propagation of moments and regularity for the Vlasov-Maxwell-Bopp-Podolsky model and its Pauli-Villars type generalizations","year":2025,"lang":"en","type":"article","venue":"Communications in Partial Differential Equations","topic":"Gas Dynamics and Kinetic Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"route_ca_aff":true,"route_ca_fund":true,"route_ca_venue":false,"route_about_ca":false,"ca_institutions":"University of Victoria","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Maxwell's equations; Type (biology); Mathematical physics; Physics; Mathematical analysis","score_opus":0.10307265298505165,"score_gpt":0.37532631427421315,"score_spread":0.2722536612891615,"validation_status":"score_only:v0-immature-baseline","prediction":{"id":"W4410098334","genre_codex":"empirical","genre_gemma":"empirical","domain_codex":null,"domain_gemma":null,"model_version":"metacan-v3-hybrid-931329e0061c","genre_candidate":"empirical","genre_consensus":"empirical","domain_candidate":null,"domain_consensus":null,"prediction_status":"machine_predicted_unvalidated","genre_scores_codex":[0.5375052,0.0022707582,0.4278388,0.0032375837,0.00024827616,0.00006341613,0.00032236037,0.00017494767,0.028338667],"genre_scores_gemma":[0.9812713,0.0007490773,0.01284518,0.00011370077,0.0001748356,0.000043654578,0.00014022,0.00004933332,0.0046125795],"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","domain_scores_codex":[0.9997502,0.00009235327,0.000011494104,0.000031252974,0.00006818405,0.00004654611],"domain_scores_gemma":[0.99842983,0.00052632566,0.00052965427,0.00014135923,0.0001529649,0.00021990258],"candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009807649,0.0004302434,0.0004945071,0.0008495856,0.00064655446,0.0013452478,0.00079786003,0.0009941572,0.001135683],"category_scores_gemma":[0.0048273895,0.00030778474,0.0006299882,0.00045354807,0.0020042325,0.0022694038,0.0013889313,0.001634615,0.00019685815],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_system_candidate":false,"about_ca_system_consensus":false,"study_design_scores_codex":[0.000035428657,0.000017467646,0.000730327,0.000043260312,0.000013455975,0.0001485342,0.00022252335,0.025227625,0.0023248421,0.9685847,0.0007170055,0.0019349775],"study_design_scores_gemma":[0.000018066898,0.000030227668,0.0006271612,0.00001564246,0.000008715411,0.00016040409,0.000080952545,0.4121625,0.00059001835,0.58528954,0.0009889267,0.000027781116],"about_ca_topic_score_codex":0.0020093312,"about_ca_topic_score_gemma":0.00095432607,"teacher_disagreement_score":0.0020093312,"about_ca_system_score_codex":0.0010497225,"about_ca_system_score_gemma":0.00054799486,"threshold_uncertainty_score":0.007616341},"labels":[],"label_agreement":null}]}