{"id":"W7116360494","doi":"10.5281/zenodo.18000814","title":"On the Infinitude of Primes of the Form a^2+1","year":2025,"lang":"","type":"preprint","venue":"Zenodo (CERN European Organization for Nuclear Research)","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Moncton","funders":"","keywords":"Constructive; Sequence (biology); Prime (order theory); Product (mathematics); Constructive proof; Prime number; Integer (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":"codex-gemma-dda1882f352a","candidate_categories":["metaresearch","metaepi_narrow","sts","open_science","insufficient_payload"],"consensus_categories":["open_science","insufficient_payload"],"category_scores_codex":[0.005419107,0.0004800823,0.000767732,0.0004587865,0.002532052,0.0004675281,0.007580957,0.0003197044,0.03025518],"category_scores_gemma":[0.01362335,0.0003235774,0.00045225,0.001538263,0.001699153,0.0001094996,0.01564189,0.001965526,0.001917595],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003661588,"about_ca_system_score_gemma":0.00009797441,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004714786,"about_ca_topic_score_gemma":0.00000104038,"domain_scores_codex":[0.9927675,0.002546972,0.001350746,0.0007723864,0.001869154,0.0006932648],"domain_scores_gemma":[0.9909823,0.001494292,0.001163273,0.00359733,0.002596913,0.0001659118],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.0004495748,0.001016281,0.00001267105,0.002632453,0.0009889991,0.000003321186,0.007123584,0.0002299176,0.001312476,0.8589829,0.111026,0.01622188],"study_design_scores_gemma":[0.001851194,0.001057308,0.0007612201,0.004242799,0.000610976,0.00005649072,0.004446719,0.002636797,0.02004334,0.4267097,0.5367122,0.0008711503],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.07689714,0.0001536383,0.004826818,0.004036388,0.0004055859,0.004936945,0.001894734,0.000311923,0.9065368],"genre_scores_gemma":[0.9792011,0.0003274427,0.0002690683,0.0001677924,0.0001189231,3.037521e-7,0.0002207496,0.001755954,0.01793864],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.902304,"threshold_uncertainty_score":0.9999216,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06614448533859008,"score_gpt":0.3014271155168925,"score_spread":0.2352826301783024,"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."}}