uniform_manifold_ops
====================

.. py:function:: t3toolbox.backend.uniform_fitting.uniform_manifold_ops(x0_data)

   .. code-block:: python

      def uniform_manifold_ops(
              x0_data:  typ.Tuple,   # UniformTuckerTensorTrain.data = (tk_sc, tt_sc, shape, (tucker_mask, tt_mask))
      ) -> bopt.GeometryOps:         # the uniform manifold geometry ops (masks of x0's fixed rank closed over)


   The uniform **manifold** ``GeometryOps`` at ``x0``'s fixed rank -- the raw-supercore twin of
   :py:data:`t3toolbox.uniform_manifold.UNIFORM_MANIFOLD`.

   ``frame`` = the orthonormal frame (:py:func:`ufv_conversions.ut3_orthogonal_representations`); ``project``
   = the gauge projection ``Pi``; ``retract`` = the manifold (doubled-rank, mask-truncated) retraction;
   ``inner`` = the masked coordinate dot (:py:func:`utv_operations.utv_corewise_inner`, the
   check-free twin of ``UNIFORM_MANIFOLD.inner`` -- equal to Hilbert-Schmidt on this orthonormal, gauged
   frame). All masks are loop-invariant at ``x0``'s rank and closed over here.