{"paper":{"title":"Mathematical foundations and numerical simulations of BDNK hydrodynamics: from heavy-ion collisions to astrophysics","arxiv_id":"2611.09582","primary_cat":"nucl-th","submitted_at":"2026-11-06T15:19:04+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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metrics.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.97,"main_claim_p":0.05,"quantitative":true,"quantitative_p":0.51,"role_probabilities":{"gap":0.0,"method":0.41,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.59,"interpretation":0.0}},{"i":2,"p":0.77,"id":"s2","own":true,"role":"result","text":"Both are hyperbolic, causal, and well-posed, pass convergence tests, and reproduce known results.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.92,"main_claim_p":0.12,"quantitative":false,"quantitative_p":0.12,"role_probabilities":{"gap":0.0,"method":0.06,"result":0.77,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.17,"interpretation":0.0}},{"i":3,"p":0.86,"id":"s3","own":true,"role":"method","text":"The first uses a new first-order reduction with mathematically preserved constraints, whose numerical violations can be handled with cleaning fields (the resulting coupled system is proven hyperbolic and well-posed).","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.86,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.14,"interpretation":0.0}},{"i":4,"p":0.64,"id":"s4","own":true,"role":"method","text":"The second uses a new mixed-order formulation, whose solutions are proven strictly equivalent to the original BDNK system, without cleaning fields.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.1,"quantitative":false,"quantitative_p":0.27,"role_probabilities":{"gap":0.0,"method":0.64,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.36,"interpretation":0.0}},{"i":5,"p":0.78,"id":"s5","own":true,"role":"contribution","text":"Our proofs rely on a new general theorem providing sufficient conditions for transforming a mixed-order system with arbitrary-order equations into a strictly hyperbolic system, strengthening a classical result by Choquet Bruhat for weak hyperbolicity.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.92,"main_claim_p":0.13,"quantitative":false,"quantitative_p":0.4,"role_probabilities":{"gap":0.0,"method":0.21,"result":0.01,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.78,"interpretation":0.0}},{"i":6,"p":0.95,"id":"s6","own":true,"role":"contribution","text":"We introduce a new practical prescription for selecting admissible hydrodynamic frames for a broad class of equations of state, including nonconformal ones relevant to heavy-ion collisions and astrophysics.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.05,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.95,"interpretation":0.0}},{"i":7,"p":0.76,"id":"s7","own":true,"role":"result","text":"Our simulations capture viscous shock broadening and suppression of Kelvin--Helmholtz vortices, reproduce Bjorken and Gubser flows, and study departures from stationary ideal-fluid configurations in Michel accretion and rotating tori on fixed Schwarzschild and Kerr backgrounds.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.15,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.76,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.24,"interpretation":0.0}},{"i":8,"p":0.74,"id":"s8","own":true,"role":"method","text":"For heavy-ion collisions, we perform boost invariant simulations with a lattice-QCD-based equation of state and fluctuating TRENTo initial conditions, comparing BDNK with a minimal Israel--Stewart 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