Demonstrates that hallucination in neural networks is a structural consequence of ungoverned superposition. Introduces a governance filter operating on the Gram matrix of the weight matrix that eliminates 100% of false-positive activations across all tested sparsity regimes (a toy-model feasibility result; true-positive retention not yet reported) in the Elhage et al. (2022) toy model framework, at a cost of 4-31% increased reconstruction error. Proposes a hierarchical two-supervisor architecture (routing supervisor + governance supervisor). No retraining, no extra parameters, applied as a post-hoc architectural layer. Originally a Google contest submission. --- **Author:** James E. Dunn — Independent Researcher, Hydrogen Lifecycle Research Programme **ORCID:** https://orcid.org/0009-0005-2679-6574 **Corpus (author search):** https://zenodo.org/search?q=creators.orcid:0009-0005-2679-6574 **SciX (NASA discovery):** https://scixplorer.org/search/q=orcid%3A0009-0005-2679-6574 **ADS (Harvard-CfA):** https://ui.adsabs.harvard.edu/search/q=orcid%3A0009-0005-2679-6574 **License:** CC BY 4.0 International