Question on Motion Representation in the First-Stage Model

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Hello! Thank you for open-sourcing this fascinating work! This project is very clear and has helped me a lot！
I noticed in the code that the first-stage model appears to use a motion representation of global root + local other key joints. For example, when computing the reconstruction loss the code seems to assume a “global root + local joints” representation: the root is reconstructed in world coordinates while all other joints are predicted in local coordinates and then transformed back to world space.
The relevant snippet is:

ric_data_gt = recover_from_ric(target_inv_trans, joints_num=self.njoints, abs_3d=self.conf.abs_3d)
ric_data_pred = recover_from_ric(model_output_inv_trans, joints_num=self.njoints, abs_3d=self.conf.abs_3d)

if self.lambda_ric_pos:
    terms["ric_pos_loss"] = self.abs_joints_loss_humanml3d(ric_data_gt, ric_data_pred, mask)

and the helper function:

def recover_from_ric(data, joints_num, abs_3d=False):
    r_rot_quat, r_pos = recover_root_rot_pos(data, abs_3d=abs_3d)  # global root rotation & position
    positions = data[..., 4:(joints_num - 1) * 3 + 4]              # local joint offsets
    positions = positions.view(positions.shape[:-1] + (-1, 3))

    # rotate local joints by inverse root rotation
    positions = qrot(qinv(r_rot_quat[..., None, :]).expand(positions.shape[:-1] + (4,)), positions)

    # add root X/Z translation
    positions[..., 0] += r_pos[..., 0:1]
    positions[..., 2] += r_pos[..., 2:3]

    # concatenate global root and transformed joints
    positions = torch.cat([r_pos.unsqueeze(-2), positions], dim=-2)
    return positions

However, the paper mentions the first-stage model uses global positions for all key joints. Could you clarify if there are additional preprocessing steps I might have missed, or if part of the pipeline is yet to be released?
Additionally, if the model is indeed trained with "global root + local other key joints", how is the trajectory-conditioned generation task for arbitrary end-effectors handled under this representation (especially when the root trajectory is not given)?
Looking forward to your insights, and thanks again for sharing the project!