ufv_variation_shapes
====================

.. py:function:: t3toolbox.backend.ufv_operations.ufv_variation_shapes(frame_data)

   .. code-block:: python

      def ufv_variation_shapes(
              frame_data:  typ.Tuple,   # uniform frame .data = (up_sc, down_sc, left_sc, right_sc, shape, masks)
      ) -> typ.Tuple[
          typ.Tuple[int, ...],          # tucker variation supercore shape = (d,) + C + (nD, N)
          typ.Tuple[int, ...],          # tt variation supercore shape     = (d,) + C + (rL, nU, rR)
      ]:


   The uniform variation supercore shapes of a frame -- the backend twin of the frontend
   ``UT3Frame.uniform_variation_shapes`` (which omits the stack; this one includes it).

   The ONE place the uniform frame-to-variation axis convention lives, so it cannot drift. The padded
   dims are read exactly as ``UT3Frame`` and :py:func:`~t3toolbox.backend.ufv_conversions.ut3_orthogonal_representations`
   read them::

       nU = up.shape[-2]    nD = down.shape[-2]    rL = left.shape[-1]    rR = right.shape[-1]    N = up.shape[-1]

   Note ``rL`` comes off the left supercore's **last** axis. Every uniform bond pads to a single ``r``,
   so the left supercore's leading and trailing bond axes happen to be equal and ``shape[-3]`` gives the
   same number today -- but that is a coincidence of the padding, not the contract, and it would break
   silently under per-edge padding. Use this function rather than indexing by hand.