{"paper":{"title":"Continuum Landscape of stable extra-dimensional metrics","arxiv_id":"2610.08006","primary_cat":"gr-qc","submitted_at":"2026-10-06T09:05:15+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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conditions.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.17,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.02,"role_probabilities":{"gap":0.0,"method":0.28,"result":0.0,"background":0.69,"limitation":0.0,"future_work":0.0,"contribution":0.03,"interpretation":0.0}},{"i":2,"p":0.84,"id":"s2","own":true,"role":"contribution","text":"For inhomogeneous metrics, we derive new stability conditions under radion excitations.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.05,"result":0.11,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.84,"interpretation":0.0}},{"i":3,"p":1.0,"id":"s3","own":true,"role":"result","text":"The central result is that stable solutions satisfying these conditions are not isolated: a typical stable regular metric belongs to a continuous family of stable metrics in its immediate neighbourhood.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.92,"main_claim_p":0.96,"quantitative":false,"quantitative_p":0.11,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":4,"p":0.98,"id":"s4","own":true,"role":"interpretation","text":"Since the effective four-dimensional physical parameters depend on the extra-dimensional geometry, this geometrical landscape of stable metrics induces a continuous landscape of effective four-dimensional parameters.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.75,"main_claim_p":0.14,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.02,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.98}},{"i":5,"p":0.96,"id":"s5","own":true,"role":"result","text":"Transitions between distinct static solutions within the landscape cannot be induced by spatially localized perturbations, whose asymptotic decay ($|x|\\to\\infty$) preserves the boundary data distinguishing the states.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.73,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.15,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.96,"background":0.0,"limitation":0.01,"future_work":0.0,"contribution":0.0,"interpretation":0.03}},{"i":6,"p":0.91,"id":"s6","own":true,"role":"result","text":"We also note a possible topological transition from a two-brane to a one-brane configuration, associated with a change in the number of regular zeros of the metric function $r(u)$.","hedge":{"p":1.0,"label":"hedged_possibility"},"own_p":0.66,"main_claim_p":0.02,"quantitative":true,"quantitative_p":0.57,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.91,"background":0.0,"limitation":0.0,"future_work":0.01,"contribution":0.07,"interpretation":0.01}}]},"compiled":{"main_claim":{"p":1.0,"text":"The central result is that stable solutions 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