Formalization of the Maximal Entropy State in the Friedmann Minisuperspace: Wheeler-DeWitt Instability and Causal Structure

We present a candidate falsifiable prediction for the spatial curvature of the universe, |Omega_k| ≈ 0.0032, compatible with the Planck 2018 bound |Omega_k| < 0.005, derived without free-parameter adjustment. The result rests on a mechanically verified formalization, in the Lean 4 proof assistant (Mathlib), of a hypothesis in which the maximal-entropy (von Neumann) state of the Friedmann minisuperspace plays the role of a timeless background from which the observable universe emerges as a partial, ongoing collapse. For flat minisuperspace (k=0) we prove normalization, exact solution of the free Wheeler-DeWitt constraint, instability for Lambda>0, and a dimensionless invariant 16/7; we extend these results to nonzero spatial curvature k, proving four further theorems, including an existential energy-compensation condition, all verified without sorry. Combining this extension with a self-consistent regularization scale and the DeWitt metric of superspace yields the curvature prediction above, together with two more speculative consequences: a structural alternative to inflationary uniformity of the early universe, and a suggestive, not established, connection to the Hubble tension. We identify precisely what blocks a formal derivation of the underlying curvature-length identification: a factor-of-order-17 mismatch between the atemporal state characteristic energy and the ground-state energy of the curved Hamiltonian on the homogeneous minisuperspace, indicating that closing this gap requires inhomogeneous perturbations absent from the present formalization. The formalization and its open problems are reported with equal precision, offering a falsifiable, mechanically checked research program in canonical quantum cosmology.