In knowledge-intensive creative tasks, Large Language Models (LLMs) often generate outputs that extend beyond established knowledge, making direct verification against current evidence impractical. Unlike factual hallucinations checked against ground truth, such outputs arise naturally in creative generation, where extending beyond current knowledge is often the goal. Yet prior work debates whether hallucination should be suppressed or embraced without empirically analyzing this unverifiable subclass. On the ideation evaluation side, existing work focuses on individual outputs without characterizing the unverifiable space as a whole. To address this gap, we propose a novelty-verifiability characterization that distinguishes Creative Synthesis (Region A) from Groundless Fabrication (Region B), and study it through a conceptual creation task where LLMs synthesize novel scientific concepts. Through 32,400 generations across three technical domains and 1,080 human judgments, we find that Region A is non-negligible (4.7%) and robust, persisting across generation strategies, models, domains, and embedding choices. A retrospective recovery experiment further shows that LLMs can approximate post-cutoff scientific concepts in controlled combinatorial settings. Our findings suggest that the unverifiable space is not uniformly noise but exhibits empirically distinguishable internal structure, providing an empirical basis for more selective hallucination governance.[<https://github.com/YuLab1/llm-concept-creation>]

LLMs often fail in hardware vulnerability detection due to the intrinsic semantic concurrency of HDLs (Hardware Description Language), where vulnerabilities arise from the interaction of multiple concurrent execution statements rather than a single sequential execution path. To address the problem, we propose VerilogLAVD, a LLM-Aided Vulnerability Detection framework by generating executable Traversal Detection Patterns (TDPs), i.e. the rules describing how to find the evidence of vulnerabilities in Verilog HDL. We first introduce a Unified Verilog Property Graph (VeriPG) that explicitly models parallel semantics by combining AST, CFG, and DDG. Furthermore, a semantic validation mechanism is designed to constrain and filter the LLM-generated TDPs. By executing these validated TDPs on VeriPG, our method produces stable and deterministic detection results. Experiments demonstrate that VerilogLAVD improves the F1 score by 133% compared to LLM-based methods. Furthermore, the framework successfully identifies real-world hardware vulnerabilities in open-source hardware design repositories.