Run a Net of Diff primitives forward and build the transposed pullback net.

Structural rows (SigCopy, SigPlus, SigDiscard, SigZero) are converted to point-independent lift pullbacks using the Diff dictionaries the constructors already carry (copy↦plus, plus↦dup, discard↦zero, zero↦discard).

Pointwise linearization: run a Net of Diff primitives forward at a and build the transposed net of pullbacks.

This is the same operation as backpropagation, but read forwards through the lens of linearize: the graph's structure is burned down into a straight linear (affine) cotangent map. Looking backwards, the single output cotangent appears to bifurcate and fan out through the wiring. Propagate fans values out in the forward direction; linearize straightens them into a wire in the reverse direction.

This is the honest reverse-mode gradient net. transpose alone is only correct for linear nets; for nonlinear Diff primitives the pullback closure depends on the primal point. linearizeAt runs the net, captures each primitive's pullback at the point it saw, and returns both the output value and a 'Net Pullback' whose wires are those pointwise pullbacks composed in reverse order.

Use evalPullback to evaluate the resulting net at a single output cotangent.

>>> let sq = Diff (\x -> (x * x, \d -> 2 * x * d)) :: Diff' Double Double
>>> let copyN = lift (Bm.copyT @(,) @Diff' @Double) :: Net (,) Diff' Double (Double, Double)
>>> let plusN = lift (Bm.plusT @(,) @Diff' @Double) :: Net (,) Diff' (Double, Double) Double
>>> let parN = widen (tensor (SMC.lift sq) (SMC.lift sq)) :: Net (,) Diff' (Double, Double) (Double, Double)
>>> let n = plusN . parN . copyN :: Net (,) Diff' Double Double
>>> let (y, g) = linearizeAt n 3.0
>>> y
18.0
>>> evalPullback g 1.0
12.0

Capture the pullback of a Diff primitive at a primal point.

>>> let d = Diff (\x -> (x * x, \dy -> 2 * x * dy))
>>> runPullback (fromDiffAt d 3) 1
6

Pointwise linearization over the core Body language.

The channel type s stays exposed, so the result can be fed directly to solveStarBody without any coercion.

Caveat: fixpoints are lazy on both passes. The forward body ties the same lazy knot as Trace Diff; the returned body ties the lazy Trace Pullback knot. For strict carriers with nonzero channel self-coupling, both diverge. The backward side can be solved in closed form by solveStarBody.