Stable Operator Displacement Fields in Learned Spaces of Polynomial Continued Fractions

A central concern in empirical studies of learned mathematical representations is whether observed geometric structure reflects a domain property or an artifact of a particular encoder. We test this for polynomial continued fraction (PCF) space by varying the latent dimension k in {3,4,5,6,7} for a family of GOTv3 geometric autoencoders and measuring the induced displacement fields of nine symbolic operators. The rank ordering of operator magnitudes is near-perfectly stable, with pairwise Spearman correlation rho in [0.967, 1.000]. Machine-precision commutator zeros persist at every k, strongly non-commuting shift/parity pairs remain large, The Apéry silence persists at 23-130x below the shift magnitude, and the latent manifold remains a near-spherical shell with z-norm coefficient of variation below 1.5%. These results provide a robustness basis for treating empirical PCF operator geometry as a reproducible phenomenon rather than a single-checkpoint artifact.