utv_probe_transpose
===================

.. py:function:: t3toolbox.backend.utv_sampling.utv_probe_transpose(ztildes, ww, frame_data, sum_over_probes=False)

   .. code-block:: python

      def utv_probe_transpose(
              ztildes,          # probe residuals, len=d, ith elm_shape=W+K+C+(Ni,)
              ww,               # probe vectors,   len=d, ith elm_shape=W+(Ni,)
              frame_data,       # UT3Frame .data (an orthogonal frame), supercore stack = C
              sum_over_probes=False,
      ):  # -> UT3Variations .data: (dU_tilde, dG_tilde, shape, masks); stack K_new + C


   Apply the transpose ``𝒥ᵀ`` of the probe map to residuals (the bare adjoint; no gauge projector).

   Mask-once the frame, pack both the residuals and the probe vectors, share
   ``probing.tv_probe_transpose`` (which routes through the 3b-6a d-prefixed WKC contractions), and
   attach the result variation masks: the frame's gauge masks broadcast over the new tangent stack
   ``K_new`` (``W+K`` if ``sum_over_probes=False``, ``K`` if ``True``). The bare ``𝒥ᵀ``.