Researchers have pursued neurosymbolic artificial intelligence (AI) applications for nearly three decades. A marriage of the neural and symbolic components can lead to rapid advancements in AI. Yet, the field has not realized this promise since most neurosymbolic AI frameworks fail to scale. In addition, the implicit representations and approximate reasoning of purely neural approaches limit interpretability and trust. Knowledge graphs (KGs), a gold-standard representation of explicit semantic knowledge, can address the symbolic side of the problem. However, automatically deriving reliable KGs from text corpora remains an open problem. We address these challenges by introducing GraphMERT, a tiny graphical encoder-only model that distills high-quality KGs from unstructured text corpora and its own internal representations. GraphMERT and its equivalent KG form a modular neurosymbolic stack: neural learning of abstractions; symbolic KGs for verifiable reasoning. GraphMERT + KG is the first efficient and scalable neurosymbolic model to achieve state-of-the-art benchmark accuracy along with superior symbolic representations relative to baselines. Concretely, we target reliable domain-specific KGs that are both (1) factual (with provenance) and (2) valid (ontology-consistent relations with domain-appropriate semantics). When a large language model (LLM), e.g., Qwen3-32B, generates domain-specific KGs, it falls short on reliability due to prompt sensitivity, shallow domain expertise, and hallucinated relations. On text obtained from PubMed papers on diabetes, our 80M-parameter GraphMERT yields a KG with a 69.8% FActScore; a 32B-parameter baseline LLM yields a KG that achieves only 40.2% FActScore. The GraphMERT KG also attains a higher ValidityScore of 68.8%, versus 43.0% for the LLM baseline.