T3Tangent.is_gauged
===================

.. py:method:: t3toolbox.manifold.T3Tangent.is_gauged(atol = 1e-09)

   .. code-block:: python

      def is_gauged(self, atol: float = 1e-9) -> NDArray:  # bool array, shape = variation stack K+C (scalar unstacked)


   True (per stack element) if the variations are gauged with respect to the frame.

   Gauge conditions (needed for :py:meth:`ManifoldGeometry.inner` / :py:meth:`ManifoldGeometry.norm`
   to equal the Hilbert-Schmidt values; not enforced at construction):

   - ``einsum('...ia,...ja->...ij', U_i, V_i) = 0`` for all i (Tucker variations ⟂ U).
   - ``einsum('...abi,...abj->...ij', L_i, H_i) = 0`` for i = 0..d-2 (TT variations ⟂ L).

   These are the gauge conditions (48)-(49), Appendix A.3, of Alger et al. (2026),
   "Tucker Tensor Train Taylor Series" (arXiv:2603.21141). **Per-stack-element bool array** (shape =
   variation stack ``K+C``; scalar when unstacked); reduce with ``.all()`` for a single verdict.