82Wosp2Iu1 / artifacts /claim2 /method.md
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Claim C1 method

This route replaces the rejected single-anisotropic-Gaussian spot check with an independently reconstructed symbolic derivation:

  1. M^T M=I gives ||Mx||^2=||x||^2 pointwise, hence equality of expectations.
  2. Haar left invariance gives QMX =_d MX for every orthogonal Q, which is the definition of spherical symmetry.
  3. Joint convexity of hockey-stick divergence under mixtures follows from convexity of the positive-part function.
  4. Conditioning on M, applying the bijection M^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.