Version of July 27th, 2026, following the technical development within the Absolute Frame Theory programme. The Absolute Frame Theory (AFT) proposes that the observable four-dimensional manifold ℳ is continuously immersed in an N-dimensional Euclidean substratum 𝒜 through a map X: ℳ → 𝒜, with gravity emerging as the entropic tension of the embedding and quantum probability as the aliasing of a deterministic pilot wave Ψ on 𝒜. We ask a single question of the assembled programme: which of its numbers are derived, and which are free inputs? We give three answers. First, a derivability audit sorts every quantity into four classes — derived structure and relations, substratum constants identified with one datum each, structurally inaccessible values, and well-posed open problems. The derived class is large and relational: the substratum dimension N = 14, the Standard-Model gauge group and its hypercharges with automatic anomaly cancellation, the ℤ₃ generation permutation and the Koide relation, the grand-unified coupling ratios and the weak mixing angle sin²θW = 3/8, the inflationary tilt and tensor ratio, and the dissolution of fundamental forces. Second, we characterize the residue. We show that the quantities AFT does not fix are, up to a small class of marginal ultraviolet-sensitive couplings, the orbit labels — dimensionful scales, phases and orientations, and topological winding numbers — under the symmetries (global rescaling, phase and rotation, large gauge) that its determining principles respect; a principle invariant under those symmetries cannot fix one of their orbit labels; hence the boundary is structural rather than accidental. Third, we reduce the residue: dimensional transmutation, acting through the induced gauge coupling, links the intermediate scales exponentially to the fundamental ones, leaving a free residue of four kinds: a choice of unit; the universal cosmological-constant hierarchy; the grand-unified gauge coupling — a renormalizable, ultraviolet-sensitive number identified by measurement rather than derived, as a companion analysis establishes; and a small symmetry-protected core of phases and the sign of the cosmic arrow of time. The non-derivable residue therefore comprises two structurally distinct sets — symmetry-orbit labels and marginal couplings. We argue that this small, largely universal residue is the substantive content of a theory of structure: the relations it fixes are falsifiable, while the absolute magnitudes are placed, with an explicit reason, beyond determination from observations confined to ℳ.
Patricio E. Valenzuela (Mon,) studied this question.