ufv_absorb_weights
==================

.. py:function:: t3toolbox.backend.ufv_operations.ufv_absorb_weights(variations, weights)

   .. code-block:: python

      def ufv_absorb_weights(
              variations: typ.Tuple,       # UT3Variations .data: (tkv, ttv, shape, masks), stack = K + C
              weights:    UT3FrameWeightsData,  # (up, down, left, right, masks), stack = C
      ) -> typ.Tuple:                      # UT3Variations .data: weighted, same shape and masks


   Absorb the four-family metric weights into the VARIATION supercores -- the uniform twin of
   ``fv_absorb_weights`` (the tangent metric on coordinates: ``down`` -> V's ``nD`` leg;
   ``up``/``left``/``right`` -> H's ``nU``/``rL``/``rR`` legs). The frame is left orthonormal and
   untouched, so this is O(ranks) and does not disturb the tangent space.

   **The weight is frame-like (stack ``C``) and the variations are ``K + C``, and the broadcast is
   free**: the ellipsis in ``'d...i,d...io->d...io'`` right-aligns, so a ``C``-stacked weight lifts over
   the tangent stack ``K`` at no cost. That works *only because* ``C`` is innermost -- the library-wide
   frame-inner convention (``docs/batching_and_stacking.md``). One metric, shared by the ``K`` tangent
   vectors at that frame.

   **No entry masking**, for the same reason as ``ut3_absorb_weights``: this is a pointwise scale along
   each edge axis, not a reduction, so garbage never mixes into a real slot (garbage-transparent). The
   reduction that follows (``utv_weighted_norm``/``_inner``) masks its own input.

   **Precondition (structural, NOT enforced here):** the weight's masks, broadcast over ``K``, must equal
   the variations' masks -- ``ufv_weights_consistent``. Uniform padding hides a mismatch that ragged
   would raise as a shape error; the frontend enforces it.