{"adoption_effect":"NONE","routes":[{"id":"R01","selected_count":16,"state":"REVIEW_SEED_NOT_SEPARATE_PROJECT","summary":"Radial extension of sphere isometries and transfer of finite-dimensional information. The route does not claim that the radial extension is linear or globally isometric; the recorded 3-Lipschitz bound is the source constant, not an optimality claim.","title":"Radial Extensions and Dimension"},{"id":"R02","selected_count":27,"state":"REVIEW_SEED_NOT_SEPARATE_PROJECT","summary":"Compact hulls, support faces, and finite lexicographic selection. The raw sets need not themselves be convex, nonemptiness is explicit, and finite-dimensional hypotheses appearing in the exact source are preserved.","title":"Compact Convex Hulls and Support Faces"},{"id":"R03","selected_count":24,"state":"REVIEW_SEED_NOT_SEPARATE_PROJECT","summary":"Maximal-minor and determinant estimates with fixed row-order and sign conventions. Ordered row embeddings are not conflated with unordered row sets, and displayed bounds are not silently reinterpreted as Euclidean operator-norm statements.","title":"Determinant Methods"},{"id":"R04","selected_count":33,"state":"REVIEW_SEED_NOT_SEPARATE_PROJECT","summary":"Piola-type identities, null Lagrangians, determinant continuity, and boundary traces. The whole-space perturbation identity concerns the integral of the determinant difference; Strong L^n includes eventual integrability, and the trace used here is pointwise on the sphere.","title":"Piola Identity and Null Lagrangians"},{"id":"R05","selected_count":14,"state":"REVIEW_SEED_NOT_SEPARATE_PROJECT","summary":"Weak gradient zero implies local and global almost-everywhere constancy, not pointwise constancy. Compact C1 test fields and divergence form the shared analytic base used by the orientation route.","title":"Weak Gradient Zero and A.E. Constancy"},{"id":"R06","selected_count":0,"state":"REVIEW_SEED_NOT_SEPARATE_PROJECT","summary":"Orientation and signed Jacobians on connected domains. No single global sign is asserted on a disconnected domain, and the null-image statement retained here is the same-dimension version present in the exact source.","title":"Orientation and Signed Jacobians"},{"id":"R07","selected_count":61,"state":"REVIEW_SEED_NOT_SEPARATE_PROJECT","summary":"Determinant-maximizing dual frames and inverse bounds, including the zero-dimensional case. Mathlib providers are preferred for norming functionals; application-specific satellite-polynomial material remains provenance rather than a new public API claim.","title":"Determinant-Maximizing Dual Frames"},{"id":"R08","selected_count":7,"state":"REVIEW_SEED_NOT_SEPARATE_PROJECT","summary":"Sphere-volume and ball-image rigidity. Compactness and inclusion in the relevant ball are explicit; equality of volume alone is not used to infer equality of sets without the separate inclusion hypothesis.","title":"Sphere-Volume Rigidity"},{"id":"R09","selected_count":20,"state":"REVIEW_SEED_NOT_SEPARATE_PROJECT","summary":"A factorization route from proportional maximal minors, retained as a heavy-refactor proof seed rather than an independently completed tool. Scale, sign, row order, and nondegeneracy conditions remain explicit to prevent degenerate overgeneralization.","title":"Determinant Factorization"}],"schema":"mathlibannex.public-route-seed.v1"}