The Illusion of Algorithmic Invariance: A Chemometric Note on the Fragility of Blind SVD in the Humanities.

This methodological note examines a critical epistemological hazard in computational humanities: a mathematically rigorous and transparent method can still produce inadequate and misleading results when its primary variance axis is dominated by semantic noise rather than stylistic signal. Using The Federalist Papers as a controlled experimental sandbox, the study shows that Singular Value Decomposition and Hotelling T-squared statistics, when calibrated with a strict qualitative filter of 11 function words, resolve the disputed authorship of Federalist 49-51 with high precision and in agreement with historical consensus. In contrast, a blind full-lexicon SVD captures thematic variance rather than authorial style; the cumulative absolute weight of thematic noise words in the loadings vector reaches 7.9742, while the share of stylistic markers falls to 0.4575. The algorithm does not fail technically but epistemologically: it faithfully finds maximum variance, which in the soft sciences often corresponds to superficial context rather than deep stylistic structure. The note warns against algorithmic epicycles and argues that qualitative humanistic constraints must be treated as explicit, auditable priors. A Specification Curve Analysis over 500 alternative analytical pathways yields a 100 percent robust Madison verdict within the local 11-word prior space, while the audit remains explicitly local rather than global. The conclusion is that without rigorous and transparent regularization of the application itself, computational analysis in the humanities risks becoming high-precision hallucination.