Explicit fold residual block

Integrate this at the residual-block level of a width-constrained MLP, small CNN bottleneck, or tokenwise transformer feed-forward sublayer. The input tensor is $X\in\mathbb{R}^{B\times T\times d}$; apply the fold independently to the final representation dimension, optionally after LayerNorm. Use either a learned center $c\in\mathbb{R}^{d}$ shared across tokens or a center generated by a small linear projection from the block input. A minimal block is: (1) $U=X-c$; (2) $V=\operatorname{ReLU}(-U)$; (3) $Y=X+2V$, which is exactly $c+|X-c|$. For a more flexible residual block, use $Y=X+\gamma W_o\operatorname{ReLU}(W_i(X-c)+b_i)+b_o$, initialize $W_i=-I$, $W_o=2I$, and $\gamma=1$, then allow fine-tuning while retaining the identity skip connection. Pseudocode is U = X - c; R = relu(-U); Y = X + 2*R; followed by the usual output projection, normalization, and dropout. The mathematical component is the exact fold initialization and its non-injectivity; learned deviations are empirical. Compare against a same-width plain ReLU MLP, a standard pre-activation ResNet block, and an invertible coupling block. First run a cheap synthetic test in $d=3$: classify two interleaved or folded curve/surface classes after projecting inputs through a width-3 bottleneck, then test CIFAR-10 with width-8 and width-16 MLP bottlenecks. Track accuracy at equal parameters, layers needed to reach a target accuracy, Jacobian rank-collapse frequency, and optimization loss. Success means the explicit fold reaches the same accuracy with fewer layers or improves fixed-width accuracy without an unstable increase in gradient norms.