A Minimal Diagram-Hilbert-Space Transformation Resolving the Quantum–Gravity Structural Inconsistency

We propose a minimal structural revision of quantum theory in which the fixed Hilbert space of quantum field theory is replaced by a diagram-indexed Hilbert space equipped with projective operators generating local degrees of freedom and topological invariants determining global structure. This single transformation resolves the core inconsistency between quantum field theory, which assumes a fixed linear state space, and general relativity, in which geometry is state-dependent and non-linear. The resulting framework produces gravity as an entropic and topological response to coarse-grained projective structure, yields particle masses via effective projective eigenvalues, and reproduces the gauge content and coupling structure of the Standard Model. Consequences include a natural renormalization-group flow toward gauge-coupling unification, protected topological sectors interpretable as dark matter, and experimentally accessible signatures at collider and cosmological scales.