Chapter 22: Boundary and Bulk-Boundary Duality

The lemniscate 𝕃 = S¹ ∨ S¹ is not merely the boundary of the central fibration τ³; it is the interface through which the interior becomes knowable. This chapter develops bulk-boundary duality as an ontological principle: the interior of a coherent region is fully determined by the structure of its boundary. The Central Theorem O(τ³) ≅ A_spec(𝕃) is the formal statement of this duality—the holomorphic function algebra on the three-dimensional fibration is reconstructed from spectral data on the one-dimensional boundary. Self and other, interior and exterior, knower and known: the boundary is the site where distinction is constituted and where interaction becomes possible. Interface philosophy is proposed as the general framework for all boundary phenomena.