Dirichlet Nulling

Dirichlet Nulling is the boundary condition that holds the pulse field at exactly zero throughout the Null-Well interior while letting it keep finite gradients on the enclosing toroidal surface. It is how the book confines physical expression to the geometric edge of a system. Inside the well the field amplitude is extinguished, which is the state of collapse in BPT; on the toroidal boundary the field's normal derivative stays finite, so activity lives there. The book presents collapse under this condition as redistribution rather than annihilation: Information Conservation, I◁ = I▷ + I_exp, keeps the information content before a pulse cycle equal to what remains after plus what is passed to expansion channels. The formal statements are Ψ(x,t) = 0 for x ∈ N(t), and ∂_n Ψ finite on ∂N(t) = T²(t), where Ψ(x,t) is the pulse field amplitude, x the spatial position, N(t) the time-dependent Null-Well interior, ∂_n the normal derivative at the boundary, ∂N(t) the boundary of the well and T²(t) the toroidal boundary surface. Dimensions: Ψ [∅], x [𝕃], N(t) [𝕃³], ∂_n [𝕃⁻¹], ∂N(t) and T²(t) [𝕃²], t [𝕋]; the book's check is consistent. It connects to the Null-Well Interior, Null-Well Boundary Condition, Strict Interior Nulling, Boundary-Only Expression, Toroidal Boundary and Information Conservation.