Self-Reference Without Collapse: Fixed Point Theory, Spectral Geometry, and Constrained Recursive Structure

The standard objection to self-referential systems is that they are circular. This paper argues that the objection asks the wrong question: the issue is not whether self-reference produces a fixed point, but whether that fixed point is trivially declared or structurally constrained by independent geometry. We instantiate the distinction concretely using the Fredholm determinant, derived from a closed set of spectral primitives through Newton’s identities. A spherical conditioning lemma proves that Pearson normalization eliminates three of four topological classes exactly, leaving the triangle as the unique surviving topology and yielding a closed-form skewness confirmed against simulation. The resulting sign inversion between correlation and covariance ensembles at identical aspect ratio provides structural evidence that the fixed point is geometrically constrained rather than tautologically specified. Updated: Non-interpretation companion file added, just the mechanism (srwc_mechanism), the main file can be safely skipped.