utv_corewise_retract
====================

.. py:function:: t3toolbox.backend.utv_operations.utv_corewise_retract(frame_data, variations_data)

   .. code-block:: python

      def utv_corewise_retract(
              frame_data,       # UT3Frame .data: the (U, G, G, G) corewise frame, supercore stack = C
              variations_data,  # UT3Variations .data: free core perturbations (dU, dG), stack = K + C
      ):  # -> retracted UniformTuckerTensorTrain .data (at the base point's ranks; stack = K + C)


   Additive (corewise) retraction: ``cores += variations``.

   The uniform mirror of the additive retraction on the corewise frame ``(U, G, G, G)`` (Section 6.3,
   Alger et al. 2026 -- the ``(P, Q, O) -> G`` substitution): recovers the point ``(U, G)`` from the frame
   (``up_tucker_supercore`` and ``left_tt_supercore``, which the corewise frame sets to the single core
   ``G``) and adds the variation supercores, giving a uniform Tucker tensor train at the base point's own
   ranks. Mirrors ``CorewiseGeometry.utv_retract`` / ``corewise.corewise_add`` -- but the uniform supercores are
   ``d``-leading (stack interior), so a ``K`` tangent stack cannot be added by plain numpy broadcasting (it
   would misalign ``d`` with ``K``): the base point (stack ``C``) is broadcast up to ``K + C`` by inserting
   ``n_K`` size-1 axes *after* the leading mode axis -- the ``K`` perturbations share one base point. The
   result masks are the frame plain-UT3 masks (``up_mask``, ``frame_left_mask``) broadcast over ``K``.