Crystal Parenthesis Expert Balancer

Integrate this after top-1 or top-2 router selection and before dispatching tokens to experts. Let router logits be g in R^(B times T times E), set w_(b,t)=argmax_j g_(b,t,j), and compute L_j as the number of tokens assigned to expert j. For every adjacent pair (i,i+1), extract positions whose labels are i or i+1 and scan them in sequence order. Maintain a stack: push an i+1; when an i arrives and the stack is nonempty, cancel one pair; otherwise record the i as unmatched. The remaining unmatched labels have the required form i^r(i+1)^s. If L_i exceeds L_(i+1) by at least two, change one unmatched i to i+1, subject to expert capacity. Process pairs in descending load difference and stop after K changes, where K is a small fraction of the batch size. The matching and legal move come directly from the paper; capacity, pair ordering, and the threshold are empirical choices. For differentiability, use the modified assignment for dispatch and retain the original router logits for backpropagation, optionally adding a straight-through gate correction. First test a 125M-parameter Transformer with top-1 Switch-style routing on a small language-model corpus. Compare against standard auxiliary load loss at equal capacity. Measure expert-load coefficient of variation, overflow and dropped-token rates, throughput, and validation perplexity. Success means at least 30 percent fewer dropped tokens and lower load variance without slower training or worse perplexity.