Version of June 2nd, 2026, following the technical development of the Absolute Frame Theory programme. We address the identification of the deterministic pilot wave that governs the dynamics on the higher-dimensional substratum A in the Absolute Frame Theory. We treat the problem as one of system identification with observables measured exclusively from within the four-dimensional manifold M, recognizing that fundamental epistemic constraints-rigorously formulated as Gödel's incompleteness theorems applied to the formal system S₀₅ₓ-preclude complete recovery of. Within this constraint, we derive the Fisher information matrix of the model for the observables currently accessible: the macroscopic coherence bound N₂ₑ₈ₓ, the quantum Fisher information FQ, and the leptonic mass spectrum. We show that the rank of the Fisher matrix is bounded by the number of independent observables, yielding a quantitative limit on the dimensionality of the identifiable subspace of. We establish a structural correspondence between singular Fisher matrices and Gödelian indecidability, and between poorly conditioned Fisher matrices and the bounded-arithmetic limitations of Buss-Paris-Wilkie. We compute explicit residuals for the harmonic-oscillator parametrization and demonstrate that no reparametrization within this family can reproduce the observed lepton mass hierarchy. We discuss alternative parametric families motivated by their spectral properties and propose an experimental-design framework based on D-optimality for prioritizing future measurements. The framework reformulates the search for from a derivation problem to a constrained identification problem, with explicit recognition of what is fundamentally inaccessible from observables within M.
Patricio E. Valenzuela (Tue,) studied this question.