Diffeomorphism invariance implies Noether identities and first-class constraints rather than ordinary global conserved charges. In a compact closed Universe with Cauchy slice Σ ≃ S³ one has ∂Σ = ∅; hence the global Hamiltonian generator associated with diffeomorphisms vanishes. Nevertheless, physically meaningful generators arise quasi-locally for subregions D ⊂ Σ with ∂D ≠ ∅ and are entirely encoded by boundary integrals. We provide a self-contained covariant phase space derivation in general relativity with an explicit Iyer–Wald Noether charge two-form Qξ and an explicit boundary three-form B corresponding to the Gibbons–Hawking–York term. For closed FRW geometry we compute the Brown–York energy of geodesic balls in Σ ≃ S³ and obtain a closed expression in terms of the areal radius R and curvature radius a(t). We relate this boundary energy to the FRW Misner–Sharp mass and clarify the role of constant-mean-curvature slicing and York time as a canonical relational clock in compact universes. Finally, we introduce a φ-discretized boundary scan Rₙ = R₀ φⁿ as a structured quasi-local bookkeeping device; a model-dependent ζφ spectral overlay and a modular reflection map n ↔ n′ are recorded separately in an appendix.
Batenin et al. (Wed,) studied this question.