LLM-as-a-Judge systems supply the reward signal in modern RLHF and RLVR pipelines, but their binary verdict reduces to a single linear readout F_gap on one hidden state. We show this readout is shallow enough that short, low-perplexity tokens flip the verdict from "No" to "Yes". These tokens are sampled from the judge's own next-token distribution at the response position, with no manual seed set and no gradient-based optimization. Our procedure, AdvJudge-Zero, reaches $>$90% ensemble false-positive rate on 22 of 24 (model, dataset) cells across six Qwen, Llama, and Gemma judges, versus 54-72% for the prior curated 10-token benchmark, and the discovered surface transfers cross-format to a 70B scalar reward model. The same discovered pool enables a defense: a LoRA fine-tune stratified by a 9-class mechanism taxonomy hardens cross-family generalization where naive sampling on the same pool fails, with mechanism breadth rather than pool size carrying the gain. Under GRPO training, the hardened judge eliminates the reward-collapse failures (false-positive spikes and length collapse) we observe in the unhardened baseline on both MATH and GSM8K at ten seeds per condition. The discovered pool, the mechanism taxonomy, and per-prompt flip records will be released under responsible disclosure.