Chapter 68: The Limit-Stage Passage

The Global Hartogs Extension Theorem (the relevant theorem, I.T06) has been proved. This chapter draws the consequences. We define earned stage-determined points (the relevant definition, I.D68) — points of τ³ whose finite-stage data is uniquely determined by omega-tail data on 𝕃 — and prove that every point of τ³ is earned in this sense (Stages from Limit, Corollary [cor:interior-from-boundary], I.C02). The algebraic lemniscate 𝕃, through its omega-tail structure, determines the fibered product completely. Finally, Passage to Book II (Proposition [prop:passage-to-book-ii], I.P29) makes the import list explicit: everything Book II needs has been earned in these 60 chapters.