Chapter 66: Thinness and the Removable Singularity Criterion

In classical complex analysis, Hartogs’ extension theorem applies to compact sets of codimension ≥ 2: a holomorphic function defined outside such a set extends across it. This chapter develops the τ-analog — primorial thinness (the relevant definition, I.D67): K ⊆ 𝕃 is thin if, at each primorial stage, it misses ≥ 2 independent CRT directions. The CRT Extension Lemma (Lemma [lem:crt-extension], I.L08) reconstructs function values locally along the missing directions. The Removable Singularity Theorem (the relevant theorem, I.T30) shows that a bounded HolFun on 𝕃 ∖ K with K thin extends uniquely to 𝕃. This is the local Hartogs extension — the global theorem follows in the relevant chapter.