Boundary Conservation Dynamics

Boundary Conservation Dynamics is the pair of equations describing reversible energy exchange between the modes living on the toroidal boundary of a Zinf-limit universe and the Null-Well reservoir inside it. The Null-Well architecture partitions reality: the interior appears physically still, with the pulse field held at zero everywhere inside (Strict Interior Nulling), though the data is not stopped there but flows through it, while all dynamic activity lives on the time-dependent boundary torus T²(t). Energy is still conserved, because it moves across the interface rather than vanishing. Boundary energy density changes through its own surface current and through two exchange rates, one carrying energy down into the interior reservoir and one bringing it back up, so nothing is lost, only transferred. The formal statements are ∂E/∂t + div_{T²}(J) = −κ⟸ × E + κ_up × ρ_N(t) and ∂ρ_N/∂t = κ⟸ × ⟨E⟩_{T²} − κ_up × ρ_N, where E(θ,φ;t) is the boundary energy density at poloidal angle θ and toroidal angle φ, div_{T²} the surface divergence on the boundary, J the surface current, κ⟸ and κ_up the positive boundary-to-interior and interior-to-boundary exchange rates, ρ_N the Null-Well reservoir proxy density and ⟨E⟩_{T²} the boundary-averaged energy density. Dimensions from the book: E and ⟨E⟩ [𝕄·𝕃⁻²·𝕋⁻²], ∂E/∂t [𝕄·𝕃⁻²·𝕋⁻³], div_{T²} [𝕃⁻¹], J [𝕄·𝕃·𝕋⁻³], κ⟸ and κ_up [𝕋⁻¹], ρ_N [𝕄·𝕃⁻³·𝕋⁻²], ∂ρ_N/∂t [𝕄·𝕃⁻³·𝕋⁻³], θ and φ [∅]. It connects to Strict Interior Nulling, Boundary-Only Expression, Null-Well Interior, Toroidal Boundary and Zinf-Limit Universe.