Book I · Chapter 70

Chapter 70: The Holomorphy Bi-Square

Page 319 in the printed volume

the relevant chapter proved that τ-holomorphic functions are natural transformations of the primorial presheaf. This chapter displays the complete structural characterization as a single pasted commuting diagram — the holomorphy bi-square (the relevant theorem, I.T41). The left square encodes tower coherence; the right square encodes spectral naturality. A family of functions is τ-holomorphic if and only if both squares commute. The Global Hartogs Theorem (I.T31) becomes the limit principle: the top row determines every bottom row. Five generators, seven axioms, one bi-square.