{"meta":{"page":1,"per_page":50,"max_per_page":100,"total":7,"total_is_capped":false,"direct_labels_cover":0,"predictions_cover":7,"direct_label_status":"direct model label, unvalidated","prediction_status":"machine_predicted_unvalidated (Codex and Gemma teacher distillation)","score_status":"score_only:v0-immature-baseline (scores rank; they never assert a category)","snapshot":{"source":"OpenAlex, pinned release, all 482 partitions","release":"2026-06-24","frame_built":"2026-07-12"},"query_hash":"fe2277027204","filters":{"venue":"PROOF"}},"results":[{"id":"W4293187703","doi":"10.37394/232020.2022.2.13","title":"The Sigmoid Neural Network Activation Function and its Connections to Airy’s and the Nield-Kuznetsov Functions","year":2022,"lang":"en","type":"article","venue":"PROOF","topic":"Algebraic and Geometric Analysis","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of New Brunswick","funders":"","keywords":"Sigmoid function; Airy function; Activation function; Boundary value problem; Function (biology); Artificial neural network; Mathematical analysis; Mathematics; Applied mathematics; Physics; Computer science; Artificial intelligence","retraction":null,"screen_n_in":null,"score":{"opus":0.02432117786437684,"gpt":0.252317565307829,"spread":0.2279963874434521,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["sts"],"consensus_categories":[],"category_scores_codex":[0.0007601595,0.00009736781,0.000135642,0.00007560712,0.002123862,0.00006769605,0.00008810528,0.00002780601,0.0001441147],"category_scores_gemma":[0.0005797587,0.00005903697,0.00005425178,0.0009158558,0.00005334758,0.00008112561,0.0001658066,0.0002245172,0.000004885907],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003267206,"about_ca_system_score_gemma":0.00001763868,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002659837,"about_ca_topic_score_gemma":0.0000495475,"domain_scores_codex":[0.9990557,0.0001741069,0.0001888366,0.0001873423,0.0002154736,0.0001784904],"domain_scores_gemma":[0.9982396,0.001356245,0.0001030124,0.0001870918,0.00006500707,0.00004903641],"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":[0.00124962,0.0002236653,0.004384876,0.00006066844,0.0009718449,0.000001316609,0.003994022,0.01769153,0.0001046563,0.7302998,0.1360821,0.1049359],"study_design_scores_gemma":[0.003239791,0.0008583135,0.01371994,0.00001856517,0.001234974,0.00006576846,0.01069492,0.0854214,0.00008426719,0.6722514,0.211773,0.0006376161],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8052376,0.005168484,0.1230806,0.05607052,0.001347717,0.002886708,0.0000173128,0.0002722284,0.005918797],"genre_scores_gemma":[0.992878,0.00002576926,0.00005290254,0.0005578194,0.0001986149,0.0003306369,0.000005008025,0.00001177573,0.00593953],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1876403,"threshold_uncertainty_score":0.9991753,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W4221014773","doi":"10.37394/232020.2022.2.11","title":"Classic Probability Revisited (II): Algebraic Operations of the Extended Probability Theory","year":2022,"lang":"en","type":"article","venue":"PROOF","topic":"Cognitive Computing and Networks","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Calgary","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Conditional probability; Probability theory; Tree diagram; Bayes' theorem; Computer science; Law of total probability; Applied probability; Inference; Probability measure; Theoretical computer science; Algebraic number; Event (particle physics); Probability distribution; Mathematics; Bayesian probability; Artificial intelligence; Discrete mathematics; Posterior probability","retraction":null,"screen_n_in":null,"score":{"opus":0.02163527867452794,"gpt":0.2407923978597869,"spread":0.219157119185259,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001964873,0.0001241305,0.0001786713,0.00003953429,0.0008511788,0.00004150249,0.001159685,0.00002960489,0.00008227005],"category_scores_gemma":[0.0003700138,0.00009048041,0.000134086,0.0009050969,0.0001557932,0.0001209874,0.002010887,0.0003584572,0.000001936499],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009179851,"about_ca_system_score_gemma":0.0002097842,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004863584,"about_ca_topic_score_gemma":0.000008851584,"domain_scores_codex":[0.9975184,0.001079254,0.0003312455,0.0004840373,0.0003559785,0.0002310984],"domain_scores_gemma":[0.9984149,0.0002223063,0.0001101845,0.0009993979,0.0002085985,0.00004459278],"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":[0.00006359972,0.00161963,0.003791016,0.0001426521,0.00007223535,0.000002418509,0.003916664,0.008593895,0.001032689,0.5246952,0.001665372,0.4544046],"study_design_scores_gemma":[0.0005828162,0.0004224241,0.03537318,0.00007342669,0.00003317081,0.00002448457,0.00004109974,0.1702829,0.003711611,0.7859544,0.003142644,0.0003578095],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6783329,0.001026498,0.306102,0.004784074,0.0008637488,0.003205813,0.00002752522,0.0003779635,0.005279534],"genre_scores_gemma":[0.9949285,0.000001151833,0.004146815,0.0003146855,0.0000408474,0.0001697594,0.000003399805,0.000006709634,0.0003881189],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4540468,"threshold_uncertainty_score":0.6546665,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W4251777843","doi":"10.37394/232020.2021.1.11","title":"Formal Theories of Engineering Management","year":2021,"lang":"en","type":"article","venue":"PROOF","topic":"Cognitive Computing and Networks","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Calgary","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Underpinning; Quality assurance; Task (project management); Workload; Work (physics); Quality (philosophy); Computer science; Knowledge management; Management science; Engineering; Process management; Systems engineering; Operations management","retraction":null,"screen_n_in":null,"score":{"opus":0.00707673609327304,"gpt":0.2063126415539966,"spread":0.1992359054607236,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001106692,0.00003853375,0.00005465494,0.00002160687,0.00002248671,0.00002067325,0.0001534555,0.00001032518,0.000004521597],"category_scores_gemma":[0.00001171955,0.00003672501,0.0000252182,0.0001690734,0.000006779901,0.00008452444,0.0003044454,0.00003682779,0.000002599525],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000004298695,"about_ca_system_score_gemma":0.00000840257,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":2.230947e-7,"about_ca_topic_score_gemma":2.299379e-7,"domain_scores_codex":[0.9996253,0.000009244046,0.00007279582,0.0001022211,0.00007626239,0.0001141354],"domain_scores_gemma":[0.9997321,0.00003359066,0.0000184038,0.0001455793,0.00005417899,0.00001617087],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.000001619689,0.00002888723,0.0001946453,0.00006276299,0.0000252214,0.00002677709,0.0002767623,0.001089774,0.0001348126,0.4339315,0.00009502451,0.5641323],"study_design_scores_gemma":[0.0008212429,0.0001173652,0.01399714,0.0004087371,0.00002550853,0.00005417848,0.000093788,0.7192317,0.197196,0.05345814,0.01413467,0.0004614625],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.007331957,0.0003880313,0.9805253,0.00008211852,0.0001899004,0.00003443889,2.152853e-7,0.00004859064,0.01139951],"genre_scores_gemma":[0.9683166,0.000008660587,0.031378,0.00003753085,0.00003082513,0.000003208856,5.307757e-7,0.000002188607,0.0002225035],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.9609846,"threshold_uncertainty_score":0.1497603,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W4406303734","doi":"10.37394/232020.2024.4.16","title":"A Note on Bivariate bi-periodic Mersenne Polynomials","year":2024,"lang":"en","type":"article","venue":"PROOF","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":1,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Manitoba","funders":"","keywords":"Mersenne prime; Bivariate analysis; Mathematics; Combinatorics; Pure mathematics; Statistics","retraction":null,"screen_n_in":null,"score":{"opus":0.01284108729815952,"gpt":0.2977949336482776,"spread":0.2849538463501181,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00006234169,0.00008805826,0.0001059249,0.0000250821,0.00007426397,0.00005638219,0.0000712117,0.00001564196,0.0006956235],"category_scores_gemma":[0.000005378839,0.00006730769,0.00006413346,0.0001293878,0.00003514186,0.00004848849,0.00002662071,0.00008855195,0.0005636314],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001058992,"about_ca_system_score_gemma":0.00002084897,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006416006,"about_ca_topic_score_gemma":1.808099e-7,"domain_scores_codex":[0.9994951,0.000008082347,0.0001208439,0.0001692267,0.00006009817,0.0001465838],"domain_scores_gemma":[0.999662,0.00008672579,0.0000206906,0.0001703343,0.00001023229,0.00004994603],"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":[0.000004044175,0.00004405247,0.000003354681,0.0000179037,0.00001860206,5.575413e-7,0.0001664722,0.00002461472,0.00209482,0.9215605,0.0003226661,0.07574245],"study_design_scores_gemma":[0.0001008526,0.00002856769,0.000006562543,0.00005415103,0.00002027901,3.787285e-7,0.00006457564,0.00121267,0.01421123,0.8529029,0.1312735,0.0001242168],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01449127,0.0002787619,0.7917816,0.004999035,0.000388354,0.0007549471,0.000170634,0.0002752588,0.1868601],"genre_scores_gemma":[0.9932569,0.00000152876,0.00363745,0.00005706439,0.0003365549,0.0001186067,0.00001000861,0.00001818173,0.002563758],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9787655,"threshold_uncertainty_score":0.7616589,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W4220758679","doi":"10.37394/232020.2022.2.10","title":"Classic Probability Revisited (I): Mathematical Models of an Extended Probability Theory","year":2022,"lang":"en","type":"article","venue":"PROOF","topic":"Cognitive Computing and Networks","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false},"ca_institutions":"University of Calgary","funders":"Natural Sciences and Engineering Research Council of Canada; Tsinghua University","keywords":"Sample space; Probability theory; Bayes' theorem; Probability distribution; Conditional probability; Computer science; Mathematics; Tree diagram; Bayesian inference; Probability measure; Applied probability; Empirical probability; Bayesian probability; Posterior probability; Artificial intelligence; Discrete mathematics; Statistics","retraction":null,"screen_n_in":null,"score":{"opus":0.04000483509680542,"gpt":0.2644729396605929,"spread":0.2244681045637875,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003080318,0.000151862,0.0002969481,0.00006229792,0.0002114357,0.00004147036,0.0009543971,0.00004119707,0.00008392158],"category_scores_gemma":[0.0001908055,0.0001360298,0.0001113076,0.0005339027,0.000130188,0.0002656399,0.001002681,0.0003260211,0.000003064067],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008262283,"about_ca_system_score_gemma":0.0001176422,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001429394,"about_ca_topic_score_gemma":6.932717e-7,"domain_scores_codex":[0.9972105,0.0009966011,0.0004261575,0.0006219394,0.0004487332,0.0002960891],"domain_scores_gemma":[0.9982092,0.0003402806,0.0001691179,0.0009861569,0.0001955936,0.00009970186],"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":[0.00009851503,0.001651956,0.0001087827,0.0002339985,0.00002760954,0.000006820722,0.001427579,0.005051796,0.0001333179,0.5674399,0.00009345744,0.4237263],"study_design_scores_gemma":[0.0001465867,0.0001806139,0.0002961167,0.00001870117,0.000006546503,0.00001102146,0.00001049823,0.4046306,0.0003290571,0.5942358,0.00003728113,0.00009711362],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1577096,0.000224132,0.836296,0.0002124329,0.00009104986,0.0009284192,0.000008400154,0.0002456924,0.004284276],"genre_scores_gemma":[0.9546173,8.585318e-7,0.04503286,0.000094251,0.00003244391,0.0001289934,0.000005278887,0.000009957635,0.00007801023],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7969077,"threshold_uncertainty_score":0.5547135,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W4412687563","doi":"10.37394/232020.2025.5.8","title":"On the Modified Standard Nield-Kuznetsov Functions","year":2025,"lang":"en","type":"article","venue":"PROOF","topic":"Mathematical Analysis and Transform Methods","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of New Brunswick","funders":"","keywords":"Computer science","retraction":null,"screen_n_in":null,"score":{"opus":0.06744060341896131,"gpt":0.3598484184583621,"spread":0.2924078150394008,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007566635,0.0001061425,0.0002164042,0.00005750271,0.0001704784,0.00003972861,0.0001543666,0.00005119826,0.0007839037],"category_scores_gemma":[0.0006811907,0.00005610072,0.0001447363,0.0003005553,0.00004056982,0.00002450163,0.00002381043,0.0001727387,0.00003009776],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001964899,"about_ca_system_score_gemma":0.00002876616,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000303358,"about_ca_topic_score_gemma":0.00001415014,"domain_scores_codex":[0.9991512,0.00009292863,0.0002464743,0.0001481106,0.0002082868,0.000152982],"domain_scores_gemma":[0.9981831,0.001312397,0.00003978315,0.0003738939,0.00005950663,0.00003131686],"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":[0.00002386849,0.00009059963,0.000005536908,0.00008072603,0.00009089609,4.717976e-7,0.00008557289,0.00001283953,0.0000313308,0.9792125,0.01158151,0.008784109],"study_design_scores_gemma":[0.00016969,0.00003721149,0.000011216,0.00005572744,0.0001103331,3.582535e-7,0.00005634391,0.002323532,0.002852971,0.9886925,0.005624884,0.00006519752],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.007542627,0.0000439846,0.6926465,0.004919899,0.00007761541,0.0003101336,0.000008110596,0.00005682292,0.2943943],"genre_scores_gemma":[0.9609461,0.000006967522,0.01072362,0.0006612981,0.00003947334,0.0001610842,0.000002082563,0.00001485938,0.02744448],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9534035,"threshold_uncertainty_score":0.8583196,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null},{"id":"W4281732905","doi":"10.37394/232020.2022.2.18","title":"A Note on Taylor Series Representation of the Nield-Kuznetsov Function of the Second Kind","year":2022,"lang":"en","type":"article","venue":"PROOF","topic":"advanced mathematical theories","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false},"ca_institutions":"University of New Brunswick","funders":"","keywords":"Taylor series; Series (stratigraphy); Convergence (economics); Mathematics; Function series; Representation (politics); Applied mathematics; Convergent series; Polynomial; Function (biology); Computation; Taylor's theorem; Mathematical analysis; Algorithm; Power series","retraction":null,"screen_n_in":null,"score":{"opus":0.03661219150660783,"gpt":0.3095382539901146,"spread":0.2729260624835068,"validation_status":"score_only:v0-immature-baseline"},"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002741215,0.00009005199,0.0001868455,0.00002421873,0.0001568394,0.000005481336,0.0002479505,0.00002845811,0.0006246345],"category_scores_gemma":[0.0008514437,0.00005277695,0.0001098827,0.0002786234,0.0001336771,0.00007964217,0.0002536429,0.0001848291,0.000001803129],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003327673,"about_ca_system_score_gemma":0.00002268892,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001415601,"about_ca_topic_score_gemma":0.00001276939,"domain_scores_codex":[0.9989216,0.0001570842,0.0003044906,0.0001331608,0.0003791446,0.0001045559],"domain_scores_gemma":[0.9985285,0.0004803231,0.0003512524,0.0005682982,0.0000586615,0.00001299611],"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":[0.0003891434,0.0003234322,0.0002574753,0.0006394775,0.00006394601,5.126586e-7,0.004940618,0.000443957,0.0235304,0.9640411,0.001134488,0.004235484],"study_design_scores_gemma":[0.0001726775,0.0001059759,0.0002348698,0.00002378406,0.00002771678,0.000003627297,0.0005338929,0.00007173663,0.2306028,0.766866,0.001308246,0.00004867893],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9438953,0.00007533898,0.0154775,0.002129288,0.001081261,0.002276532,0.0001218733,0.00007351336,0.03486943],"genre_scores_gemma":[0.9929235,3.908572e-7,0.001848058,0.00007699645,0.00003031271,0.0001042455,9.840631e-7,0.00001810935,0.004997408],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2070724,"threshold_uncertainty_score":0.683931,"prediction_status":"machine_predicted_unvalidated"},"labels":[],"label_agreement":null}]}