The Derivable and the Gödelian: Structure versus Scale in Absolute Frame Theory

A common expectation of a fundamental theory is that, were it complete, it would compute every number nature exhibits: a "theory of everything" should imply every value. We argue, from within Absolute Frame Theory (AFT), that this expectation is mistaken in a precise and unified way. AFT derives the structure of the world---its symmetry groups, representations, functional forms, mechanisms, and the signs and existence of nature---while a sharply delimited set of scales, phases, and magnitudes is irreducibly internal to the substratum A and therefore undecidable from observations confined to the observable manifold M (the Gödelian sector). This split is not an ad-hoc limitation but a structural law with a single root. We give that root two complementary statements. The first is kinematic: action quantization (Axiom I) fixes first moments---capacities, positions, group data---and not second moments, while the observable normal connection of the embedding is flat, whence every non-trivial holonomy is an onset datum. The second is dynamical and is the core of the paper: in AFT, cosmological inflation is the relaxation of the embedding map---a harmonic-map gradient flow in the sense of Eells--Sampson---under which the continuous initial data are forgotten exponentially while the topological (kernel) data are conserved. We state and prove exhaustively a forgetting theorem: along the L²-gradient flow of the embedding's Dirichlet energy with routing potential, the Fisher information about each non-zero mode decays as e^-2ₖ t, the Cramér--Rao bound for reconstructing it grows as e^+2ₖ t (an ill-posed backward-heat inversion), and the zero mode is conserved. A corollary extends the theorem to M independent measurements at distinct times: the Fisher information is additive, yet the variance bound remains exponential in the earliest measurement time, and a channel of finite observation rate caps the recoverable information uniformly in M. The derivable equals the kernel; the G\"odelian equals the decaying sector. We then exhibit five frontiers---the leptonic mixing matrix, the macroscopic decoherence knee (N), Pati--Salam unification, the seesaw B-L scale, and the baryon asymmetry B---each splitting along the same line: derived structure, Gödelian scale. A further case is derived rather than classified: for p2 particles sharing a substratum point (Axiom II), the joint state is a diagonal modal sum whose Schmidt coefficients, across every bipartition, are the modal projection weights of the shared point. Falsifiability accordingly resides in the structure---the functional forms, the erfc knee, the prediction ²W=3/8, the symmetries---not in the values. We close by distinguishing the classical "predict every number" goal, limited here by construction, from the structural goal AFT can meet, and by treating the explicit drawing of this boundary as the epistemic seal of the program.