Chapter 12: The Parity Bridge Theorem

The 4+1 decomposition assigns each generator a sector of the spectral algebra. But not all sectors are created equal. Each primitive sector projects differently onto the two lobes of the lemniscate 𝕃, and this asymmetry has a measurable consequence: spectral polarity. Three of the four primitive sectors are polarised—they project predominantly onto one lobe. The weak sector Sector π alone is balanced: it projects equally onto χ_+ and χ_-. This chapter proves that balanced polarity is the unique structural prerequisite for the E₁ → E₂ transition. The Parity Bridge Theorem identifies the weak sector as the canonical carrier of the computational bootstrap. We close with a conjectural reading: the weak force’s identity-changing character in particle physics is the physical shadow of the code–execution–code cycle that defines operational closure.