Structural Constraints on Observable Algebras from Finite-Rank Non-Invertible Projections

DECRIPTION: This paper establishes four structural consequences of finite-rank non-invertible projections, valid model-independently under four minimal hypotheses, without assuming any specific field content or dynamical law: (i) The kernel of the bulk-to-boundary map is infinite-dimensional. Distinct bulk configurations generate identical boundary observables exactly, not approximately. (ii) The boundary observability capacity is finite and interface-specific, providing a model-independent upper bound on recoverable bulk information structurally analogous to Shannon's channel capacity. (iii) The absolute dimensional scale belongs to the kernel of the adjoint projection Π∗Π∗. The boundary algebra is adimensional by structural necessity. A single metrological anchor — internal to the boundary sector but external to the adimensional subalgebra — is necessary and sufficient. (iv) In the fully incoherent limit, residual boundary correlations are scale-free: S(ω)∝ω−1S(ω)∝ω−1. The 1/f1/f floor is the irreducible observable signature of the kernel. These results are derived first for wave systems at strongly asymmetric interfaces and then extracted as a general model-independent framework. They provide the model-independent mathematical framework on which the QGT programme is built as a specific physical realisation under the identification Π:M5→R4Π:M5→R4.