Drawing on the proof strategy of the three-dimensional Kakeya theorem, the design requires candidate evidence to persist in disjoint data and to withstand capacity-matched substitutions of physical organization or listener templates. Across six EEG datasets (41 participants), averaging four neural-speech margins improved 5-second decoding relative to the leading margin in three evaluation sets whose rules were fixed before results were computed (study-equal gain, 0.0201; 95% interval, 0.0125-0.0279).
In three continuous-speech datasets (43 participants; 86 directed transfers), listener-matched weights outranked other-listener weights by 0.0969 and wrong mappings by 0.1371, although accuracy did not improve universally. In two hierarchical interfaces, a parent-stream error score retained AUCs of 0.968 and 0.965 after oracle-label exclusion of all target-command events, outperforming an EOG-only comparator and depending on the physical command-stream mapping. Eight electrodes retained 59-77% of binding specificity, but one listener-consistency criterion failed.
The authors state that the main contribution is a transferable standard for testing what information supports a decoded psychological construct. The framework does not prove that attention is the only cause; it offers neuroscience and brain-computer interfaces a standard: evidence should transport, its proposed organization should matter, and credible shortcuts should fail.