t3_left_orthogonal_norm_sq
==========================

.. py:function:: t3toolbox.backend.geometry.t3_left_orthogonal_norm_sq(x_cores)

   .. code-block:: python

      def t3_left_orthogonal_norm_sq(
              x_cores:  typ.Tuple,   # (tucker_cores, tt_cores) -- a LEFT-orthogonal T3 (a frame's (U,P), or a retracted point)
      ) -> NDArray:                  # ‖X‖²_HS, shape = stack C (a 0-d scalar for C=()); PER-ELEMENT over the stack


   ``‖X‖²_HS = ‖last TT core‖²`` -- exact for a left-orthogonal T3 (the frame's ``(U,P)`` or a
   ``t3svd`` retraction output), so no dense tensor and no re-orthogonalization. The left-orthogonal
   precondition is check-free here (backend) and is the caller's responsibility: on a raw point the value
   is simply wrong (measured 3 vs 1400 on a ``randn`` point -- the 2026-08-22 review). Use
   :py:meth:`ManifoldGeometryOps.point_norm_sq` for an arbitrary point; verify a point with
   :py:func:`t3toolbox.backend.t3_orthogonalization.t3_orthogonality_residual`.
   (``docs/contributor/fitting_internals.md`` §"The base point as a tangent".)