Large language models (LMs) store vast factual knowledge, yet turning it into a reliable, set-valued knowledge base, where a subject may have zero, one, or many objects, remains hard. The AKBC 2026 shared task (5th LM-KBC edition) poses this in a strict closed-book setting: an open-weight model of at most 32B parameters, with no retrieval, no external knowledge, and no fine-tuning. We start from the metric and observe that it rewards abstention: since an empty prediction scores a perfect F1 against an empty gold set, predicting nothing everywhere already reaches 0.169 relation-averaged macro-F1, and on the null-heavy relations even beats the official baseline. We therefore treat when to answer as a first-class decision and build a per-relation pipeline that grounds each prompt in the relation’s exact scope, decides abstention from the sampled set rather than by instruction, and takes a median over samples for numeric relations. Our Gemma-4-31B system (30.7B, the strongest in-budget model we could access) scores 0.461/0.488 (relation-averaged/micro) on validation from a single sample, beating the official baseline on five of the six relations, while a smaller 4-bit Qwen2.5-14B, even with self-consistency voting, reaches only 0.415: in this comparison a larger single-sample model outscores a smaller voted one. Generation is cached, so decoding reproduces without a GPU. We release all code, prompts, and cached generations: https://github.com/minhaz-42/lm-kbc-2026