Pre-Invariance: Extending the Axiomatic Eigenvector Framework

Epistemic evaluation typically begins with intelligibility: an articulation is either meaningful and therefore eligible for assessment, or it is noise and excluded from consideration. This binary obscures a class of articulations that exhibit stable internal structure yet fail to achieve external stabilization. This paper introduces epistemic eligibility as a prior criterion, formalized through a dual variable model distinguishing internal invariance from external stabilization. The resulting category, the Pre-Invariant, captures articulations that conserve structure without translation into shared epistemic space. Building on the invariance-based epistemology developed in Mathematics as Contemplative Science [1], this framework distinguishes two modes of epistemic emergence—correction and discovery—and introduces a resolution parameter that models delayed intelligibility as an environmental rather than intrinsic shift. The framework is illustrated through analyses of mad speech and pre- scientific anomalies, and concludes with clarifications addressing common objections. The aim is to provide a minimal, structural account of how knowledge emerges from structured opacity without presupposing semantic content or predictive guarantees.