Chapter 1: The Boundary-First Paradigm

Classical several complex variables (SCV) flows from interior to boundary: one starts with holomorphic functions on open domains and derives boundary values as limits. Category τ inverts this flow. Book I earned a boundary object—the algebraic lemniscate 𝕃—and a holomorphic calculus on it, then proved that boundary data determines interior structure (Global Hartogs Extension). This chapter explains why the inversion is not a stylistic choice but a structural consequence of the coherence kernel, catalogues the five exports from Book I that power Book II, and states the Boundary-First Principle as a formal remark.