Chapter 63: What Survives the Fork

the relevant chapter established that a single sign—j² = +1 versus i² = -1—rewires twelve levels of mathematical structure. This chapter asks the complementary question: what survives?

Two modes of the five-mode framework answer this. Mode A (Same) identifies constructions that are literally identical between τ and orthodox mathematics. Mode B (Parallel) identifies constructions that satisfy the same defining axioms but live on different carriers.

Together, Modes A and B provide the reassurance that Category τ is not an alien framework. The primes are the same primes. π is the same transcendental. Holomorphic functions satisfy the same axioms. What changes is the substrate—not the mathematical content.