Version of July 10th, 2026, following the technical development of the Absolute Frame Theory programme. We address the identification of the deterministic pilot wave Ψ 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—associated with the Gödel phenomenon, in that under declared premises the AFT substratum has the expressive capacity to encode undecidable arithmetic—limit complete recovery of Ψ. Within this constraint, we derive the Fisher information matrix of the model for the observables currently accessible: the macroscopic coherence bound Ncrit, 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 Ψ. We propose—as a conjecture, a quantitative theorem left to future work—a structural correspondence between singular Fisher matrices and Gödelian undecidability, and between poorly conditioned Fisher matrices and the bounded-arithmetic limitations of Buss-Paris-Wilkie; since Fisher singularity is generic to any non-identifiable model, the correspondence is offered as an operational proxy for the framework's declared inaccessibility, not as an established equivalence. We compute explicit residuals for the harmonic-oscillator parametrization and demonstrate that, under the natural assignment of the three charged leptons to the three lowest modes, 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 Ψ from a derivation problem to a constrained identification problem, with explicit recognition of what is fundamentally inaccessible from observables within M.
Patricio E. Valenzuela (Fri,) studied this question.