Canonical-Closure Defects Across the Condensate-to-Matter Reduction in Relational GFT Cosmology

A recent five-scalar group-field-theory (GFT) cosmology derives an emergent FLRW geometry and an effective scalar-matter equation from a relational quantum-gravity condensate. The construction passes through distinct reduction layers: a complex condensate mean field, its density-phase hydrodynamics, and finally an emergent scalar perturbation obtained by readout and partial elimination of hydrodynamic variables. This paper asks where, along this chain, a source-compatible local canonical description is actually established. The sharpest source-specific result is an exact density-phase cross-adjoint identity. For a Fourier mode, the phase-to-density and density-to-phase cross operators obey Lk+ρ0−2Dk†=−2β/ρ0L_k+ρ_0⁻²D_k^=-2β/ρ_0. Thus the weighted adjoint pairing is exact in the decoupled branch β=0β=0 and fails by a fixed residual when the coupled branch is activated. The corresponding Layer-B symplectic-preservation defect is shown to be the two-form image of the same Hamiltonian-closure obstruction. Independently, at the condensate layer, the finite-kk αiα_i term produces a formal-adjoint defect and excludes a positive-definite real local matrix Helmholtz multiplier. At the emergent-matter layer, each Fourier mode can be variationalized by an integrating factor, but the gradient-dependent friction makes this factor kk-dependent and hence generically spatially nonlocal in position space. Exact density elimination additionally produces Green-function dependence, memory, and a homogeneous inverse fibre. The paper therefore does not claim that the microscopic GFT is non-Hamiltonian or that the published damping term proves fundamental irreversibility. Its claim is that the coupled matter phenomenology is derived, while source-native canonical closure is not automatically preserved through the condensate-to-matter reduction; the missing canonical or influence data must be recovered at the layer where they are lost.