The Cohomology Language: How the Compiler Specifies Its Output

Papers 135–138 established the quintic compiler (the mechanism by which A₅ non-solvability converts algebraic input into topological output) and showed that the Riemann Hypothesis, BSD, the Tate conjecture, and Bloch–Kato occupy rows of a single compilation table. This paper identifies the language of the compiler. The BSD conjecture Part II specifies the exact leading term of the L-function of an elliptic curve as a product of five factors: period, regulator, Tamagawa numbers, the order of the Tate–Shafarevich group, and torsion. We show that the same five-factor format appears at every row of the compilation table — BSD (β₁), Tate (β₂), and Bloch–Kato (β₃) — with each factor playing the same structural role.…