{"paper":{"title":"Stability of Collective Neutrino Oscillations -- A Distributional Approach","arxiv_id":"2609.04441","primary_cat":"hep-ph","submitted_at":"2026-09-03T20:01:45+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. 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sphere.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.07,"quantitative":true,"quantitative_p":0.56,"role_probabilities":{"gap":0.0,"method":0.71,"result":0.09,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.2,"interpretation":0.0}},{"i":2,"p":0.52,"id":"s2","own":true,"role":"method","text":"This equation admits a two-parameter family of azimuthally symmetric stationary solutions, whose stability we analyze by linearizing around them.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.88,"main_claim_p":0.06,"quantitative":true,"quantitative_p":0.63,"role_probabilities":{"gap":0.0,"method":0.52,"result":0.29,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.19,"interpretation":0.0}},{"i":3,"p":0.47,"id":"s3","own":true,"role":"contribution","text":"The resulting eigenvalue condition determines the growth or decay rate of small perturbations from \\emph{any} initial distribution -- not merely from a state close to full flavor coherence -- thereby going significantly beyond the conventional linear stability analysis of collective modes.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.49,"quantitative":false,"quantitative_p":0.47,"role_probabilities":{"gap":0.02,"method":0.01,"result":0.17,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.47,"interpretation":0.33}},{"i":4,"p":0.78,"id":"s4","own":true,"role":"result","text":"In special limits the condition reproduces known synchronization thresholds in the two-beam model, providing a non-trivial check of the framework.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.86,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.36,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.78,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.03,"interpretation":0.18}},{"i":5,"p":0.81,"id":"s5","own":true,"role":"contribution","text":"We present analytical results for the eigenvalue equation and explore stability phase diagrams for physically relevant frequency distributions.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.11,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.19,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.81,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":1.0,"text":"The resulting eigenvalue condition determines the growth or decay rate of small perturbations from \\emph{any} initial distribution -- not merely from a state close to full flavor coherence -- thereby going significantly beyond the conventional linear stability analysis of collective modes.","location":"abstract s3","hedge_strength":{"p":1.0,"label":"asserted"}},"provenance":{"route":{"via":"TypeSafe API","model":"classifier-1.13.0","endpoint":"https://api.typesafe.ai/v1/systemone","provider":"TypeSafe"},"packing":"one request per 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