UniformManifoldGeometry.retract
===============================

.. py:method:: t3toolbox.uniform_manifold.UniformManifoldGeometry.retract(p)

   .. code-block:: python

      def retract(
              self,
              p:  UT3Tangent,   # step (a tangent at the current point's frame)
      ) -> ut3.UniformTuckerTensorTrain:  # retracted point on M, at p's frame ranks


   Retract the step ``p`` to the manifold: shifted doubled-rank embedding, truncated to frame ranks.

   Forms ``base point + p`` and truncates back to ``p``'s frame ranks via the implicit uniform T3-SVD
   (Algorithm 10). The current point is carried by ``p.frame``, so no separate point argument is needed.
   **Safe mode** requires ``p``'s frame orthogonal (raises otherwise; skipped under ``safety.unsafe()`` /
   a jax trace). ORTH only -- retract is gauge-invariant; minimal rank is a documented caveat.