Large language models (LLMs) have enabled more effective vulnerability scanning of web applications. However, these capabilities also make it significantly easier for attackers to automate cyberattacks on the web. In this work, we investigate how to divert malicious LLM-based web scanning, with preservation of genuine functionality as a deployment requirement. We systematically study six LLM-based scanners and summarize how they gather information and iteratively select actions based on observations. Guided by the study, we then present WebMaze, a defense that preserves genuine application functionality while diverting LLM-based scanners to a generated decoy world. WebMaze embeds functionality-coupled traps in genuine pages and constructs view-tailored interactive decoy worlds from the application's existing views. The traps blend into genuine components and expose entry points to decoy worlds that sustain exploration through connected pages and interactions without changing genuine functionality. Across 12 web applications and three LLM-based scanners under the default no-disclosure setting, decoy pages account for an average of 93.0% of the distinct pages requested per run. This demonstrates that WebMaze effectively diverts scanners away from genuine application pages and into the generated decoy worlds. Even when explicitly informed about the decoy mechanism and instructed to avoid decoy pages, scanners continue to explore predominantly decoy pages.
For masked rank-one least squares with unrestricted signs, gradients reveal weighted margins and the loss reveals the target's squared norm. We prove that this one scalar resolves the gradient ambiguity on bipartite cycle and length-three parallel-path blocks: every target fixed before sampling and nonzero on cycle edges is identified almost surely by one legal positive query drawn from an absolutely continuous law. On six-cycle flowers, open target and query sets retain $3^r$ bounded gradient candidates. A common algebraic witness excludes cross-block energy cancellation. Cactus masks admit explicit exception certificates and target-uniform finite-grid bounds; theta blocks admit an existence guarantee. For nondegenerate cactus reductions, an exact decoder returns complete actual real lists, with bit cost polynomial in input length, the cycle-degree product $D$ and the optional budget parameter $2^κ$. Energy-coordinate propagation certifies singletons without a product join. The product $D$ can grow exponentially in cycle count. Exponential certificate-degree and output bounds, and weak NP-hardness at a fixed uniform query, characterize distinct costs of exact decoding.