utv_probe_transpose

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

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.