How Many Labelled Trials Is Euclidean Alignment Worth? A Within-Corpus Dose-Response for EEG and EMG Transfer

Euclidean Alignment (EA) and its Riemannian relatives are near-universal preprocessing in EEG and EMG decoding, and are reported as accuracy gains over an unaligned cross-subject baseline. That baseline answers the wrong question. The question a practitioner faces is not does alignment help? but is borrowing donor data worth more than labelling a few trials from this user?, and answering it requires a column the alignment literature does not report: an in-domain k-shot decoder trained on the target subject alone. Across ten public configurations and 36 within-corpus cells, the crossing budget—the number of labelled target trials at which the in-domain decoder reaches the aligned cross-subject one—ranges from 12 to over 240 total trials and depends on the decoder, so no single constant answers the question and a paper reporting a gain without this column has not reported enough. We characterise what governs the budget. It is not class count: a between-corpus ordering by K looked compelling and was refuted by the withincorpus dose-response we ran to test it, which finds k * falling with K on high-SNR sEMG and flat on low-SNR EEG-MI. It is not modality either. What our data leaves standing is within-subject decodability, measurable in advance—though we show only that class count does not govern the budget, not that decodability does. Priced for the decoder a practitioner would actually deploy—tangent-space logistic regression on both arms, with the in-domain arm touching no donor data at all—the budget is 18–40 total labelled trials on every corpus tested, a 2.2× band across two modalities and K in 2, 4, 6. Read per user rather than per corpus, 60 total trials reaches the aligned level for 87% of sEMG and 70% of EEG-MI subject-cells, with 10% and 22% served by no tested budget—a ceiling set by our grid rather than an observed asymptote, and a lower bound on what the cross-subject route costs. All of this is interpretable only against a calibration of zero, which is the paper's second contribution: when the alignment reference and the fit are both in-domain, the gain is identically zero for any decoder invariant to the corresponding congruence—a two-line consequence of affine invariance, exact, falsifiable by one trial changing one label, and holding on 137 subject-fits (119 above a pre-declared informativeness floor) on two classifier families at every regularisation tested. A factorial then separates the two knobs the literature conflates: the reference governs exactness, the fit governs magnitude.