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Claim C1 method
This route replaces the rejected single-anisotropic-Gaussian spot check with an independently reconstructed symbolic derivation:
M^T M=Igives||Mx||^2=||x||^2pointwise, hence equality of expectations.- Haar left invariance gives
QMX =_d MXfor every orthogonalQ, which is the definition of spherical symmetry. - Joint convexity of hockey-stick divergence under mixtures follows from convexity of the positive-part function.
- Conditioning on
M, applying the bijectionM^T, and using||M^Tv||=||v||bounds every symmetrized shift by the original worst-direction supremum.
The verifier checks the dependency DAG, exact symbolic isometry algebra, the two exhaustive sign cases for positive-part convexity, and three intentionally invalid mutations.