compute_sigma_hat
=================

.. py:function:: t3toolbox.backend.probing.compute_sigma_hat(right_tt_cores, xis, c)

   .. code-block:: python

      def compute_sigma_hat(
              right_tt_cores: typ.Sequence[NDArray],  # Q.  len=d, elm_shape=C+(rRi,nUi,rR(i+1))
              xis:            typ.Sequence[NDArray],  # frame up-index edge vars, len=d, elm_shape=W+C+(nUi,)
              c:              NDArray,                # residual (scalar), shape=W+K+C
      ) -> typ.Sequence[NDArray]:                     # sigma_hats. len=d, elm_shape=W+K+C+(rR(i+1),)


   Propagation-only adjoint **reverse** sweep via ``Q``, seeded at the terminal bond by the residual
   ``c`` -- the order-0 (non-jet) analog of :py:func:`t3toolbox.backend.sampling_derivatives.compute_sigma_hat_jets`.

   The right context the apply/entries transpose needs, **recomputed** from ``c`` rather than stored:
   this is the low-memory half of the adjoint-state method (no ``nu``/``eta`` precomputed). ``sigma_hats[i]``
   is the adjoint of the after-core-``i`` carry; it carries the tangent stack ``K`` (from ``c``).
   Right-to-left via ``tt_reverse`` (mirroring the forward ``nu`` sweep's reversal).