Supple: How Beierspace Extends Eigenspace

The covariance matrices on which modern financial economics depends are composed predominantly of human-decision-determined quantities. Their eigendecompositions are temporary. This paper formalizes the consequences. A stability condition S = LD/(sigma_e + sigma_b(LD)) is derived from a network model of heterogeneous agents, where L is aggregate learning capacity, D is aggregate disclosure rate, sigma_e is the rate of physical structural change, and sigma_b is the rate of human-generated structural change. The central result is that sigma_b is itself a strictly decreasing function of LD: the agents whose learning and disclosure determine whether structural change is detected are the same agents whose decisions generate the structural change. This reflexive feedback produces a phase transition at S = 1 with an unstable fixed point, self-stabilizing dynamics above the threshold, and self-destabilizing dynamics below it. The corrected dynamics with bounded re-entry exhibit a saddle-node bifurcation at a computable critical parameter mu_crit. Below mu_crit, the system has two stable equilibria: a collapse trap and a well-functioning state. An informational impossibility result follows: a system in the collapse trap cannot determine from its own data whether its collapse is permanent or recoverable, because the parameters distinguishing these regimes are not identifiable from crisis outcomes. These results hold for any continuous, strictly decreasing Beier drift function, not only the specific parameterization used for computation. The paper further shows that cognitive suppleness - the capacity to absorb large model revisions without degraded learning - unconditionally amplifies stability and conditionally expands the usable dimensionality of the eigenspace when drift rates fall within the attention budget. The suppleness multiplier is derived from established results in cognitive psychology on belief updating under disconfirmation. From the Prolegomena to the Unification of Economics, Computer Science, Mathematics, and Physics by Gregory Caldwell Beier (forthcoming 2026).