Chapter 31: The BndLift

This chapter constructs the central operator of Part VI: the boundary lift BndLift_n, which promotes boundary data at stage n to interior data at stage n+1. The construction uses the Chinese Remainder Theorem on primorial completions (I.T18, Book I) to decompose the lift into two independent channels. The bipolar idempotents e_± = (1 ± j)/2 (II.D33, the relevant chapter) split the lift into a B-sector component and a C-sector component, each governed by its own calibration constant (π for B, e for C). The coupling between the two channels is controlled by the master constant ι_τ = 2/(π + e) (I.D24, Book I; II.T25, the relevant chapter). The main results are: the lift exists , it is unique (forced by CRT and the diagonal discipline K5), and the two channels are independent (Proposition [prop:bipolar-channel-independence]). The BndLift_n is the engine that drives the Local Hartogs extension: iterating the lift produces interior holomorphic data from boundary data, one stage at a time.