check_fw_pair
=============

.. py:function:: t3toolbox.frame_variations_format.check_fw_pair(frame, weights)

   .. code-block:: python

      def check_fw_pair(
              frame:   T3Frame,          # stack_shape = C (frame/core stack)
              weights: T3FrameWeights,   # stack_shape = C -- a weight is FRAME-LIKE: one metric per base point
      ) -> None:


   Check that ``weights`` is a metric on the tangent coordinates **at this frame**.

   The weight<->frame analog of :py:func:`check_fv_pair`. A :py:class:`T3FrameWeights` is **frame-like**:
   it carries the frame stack ``C`` (one metric per base point, shared by every tangent there), and its
   four families weight the variation holes ``frame`` leaves -- ``up``<->``nU``, ``down``<->``nD``,
   ``left``<->``rL``, ``right``<->``rR``. So the stack must match ``frame.stack_shape`` **exactly** (not
   merely be a trailing part of it, as when pairing with variations alone).

   Why the stricter check lives here: absorption only needs the weight's stack to be the *trailing* part
   of the variation stack (:py:func:`~t3toolbox.backend.fv_operations.fv_weights_consistent`, which is
   blind to the frame, like the variations themselves). A ``K + C``-stacked weight also satisfies that --
   it reads as ``C_w = K + C`` (that many base points, one tangent each), a legitimate absorption -- so it
   would silently weight a ``C``-framed tangent's ``K`` coordinates with ``K`` *different* metrics. This
   is the only place where both objects are present, hence the only place with enough information to
   reject it. Structural (shapes only) -> raises in both safety modes; jit-safe.