SOACT: Square-free Orthogonal Action Composition and Transport for brain-free answer prediction

Brain-guided language models align neural representations, but alignment alone does not specify how registered actions change a latent state or compose. SOACT predicts fixed-vocabulary answers from text using a minimal square-free quotient and registered action transport under an external action plan. It estimates nuisance-invariant moments from same-question cross-subject views using square-free products, fits polynomial action generators in a shared chart with no free intercept, composes ordered paths by substitution, and trains a text readout with the generators frozen. Independent composed-action anchors provide a proposed score-calibrated factorization test, with abstention when the evidence is unresolved. Under centered conditional noise and cross-subject independence, we show that square-free moments recover latent polynomial moments; a two-world lower bound identifies information lost by row-separable temporal objectives. We also characterize the degree identified by finite view panels and derive a scoped ($2d$) versus ($2d^2$) view-count comparison for factorized and primitive path fitting. The experiments use fixed-seed synthetic latent states, paired noisy views, action compositions, and matched comparator protocols. The reported values are evaluated under the declared experimental contracts. The task, ablation, gate, and sensitivity evaluations show the performance of SOACT and the matched non-emulating baseline under the stated protocols.