Falsifiable substitution tests reveal task-structured neural evidence for auditory attention

A neural decoder can predict a mental-state label without using information specific to that state. We made auditory- attention attribution falsifiable by requiring candidate evidence to persist in disjoint data yet change under capacity- matched substitutions of physical organization, listener or population template, target response, or command identity; two event-related datasets also permitted electrooculography (EOG)-only comparisons. The design drew on Wang and Zahls three-dimensional Kakeya proof strategy: examine the organized family and its concentration, not only the strongest member. Across six EEG datasets, averaging four neural-speech margins improved 5-s decoding relative to the leading margin in three evaluation sets whose rules were fixed before their results were computed (41 participants; study-equal gain, 0.0201; 95% interval, 0.0125-0.0279). A 16-cell scalp-direction-delay representation replicated in a participant-disjoint cohort and exceeded the mean of 15 capacity-matched remappings. Across 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. It depended on the physical command-stream mapping, exceeded an EOG-only comparator, and generalized within listeners after training-only removal of command identity. Eight electrodes retained 59-77% of binding specificity, but one listener-consistency criterion failed. The main contribution is a transferable standard for testing what information supports a decoded psychological construct. Significance StatementInspired by the proof strategy of the three-dimensional Kakeya theorem, we turn "a neural decoder reads auditory attention" from an interpretation of accuracy into a falsifiable test of evidence attribution. Engineering can exploit any stable predictor; science of latent mental constructs must ask whether the proposed construct remains necessary after plausible alternatives are removed or substituted. Across six electroencephalography (EEG) datasets, task-organized scores survived disjoint data yet changed when physical mapping, listener template, target response, command identity, or eye-movement signal was replaced at matched capacity. This framework does not prove that attention is the only cause. It offers neuroscience and brain-computer interfaces (BCIs) a standard: evidence should transport, its proposed organization should matter, and credible shortcuts should fail.