Addendum to Paper~I: Six Gap Closures for the Master Equation Framework.

We present the Master Equation, a generalisation of Einstein's field equations derived from a 12-dimensional Riemannian manifold. This addendum collects Seven self-contained gap closures for Paper I of the Master Equation Framework (MEF). Each section addresses a specific foundational issue identified during peer-review-level critique of the framework's core field equation, GMN = 8π Geff TMN + ζ ∇M Q ∇N Q + Λeff gMN , where Q = ω(ψ - ψ̄)² is the Quantum Coherence Dilaton, ω is the negentropic order parameter, ψ and ψ̄ are the quantum and anti-quantum spinor condensates localised at the Quantum-wall and Anti-Quantum-wall of the T²/Z₂ orbifold, and ζ = 12π is the quantum coherence coupling constant derived from χ(K₈) = 12. The Seven closures are: (§1) uniqueness of the dilaton form Q = ω(ψ - ψ̄)²; (§2) dynamical condensation of the fermionic zero modes; (§3) the π-per-flux-unit result from a reduced 2D BPS equation; (§4) extension to the full 8D fibre; (§5) the Weinberg angle from an explicit Kaluza–Klein integral; (§6) hypercharge quantisation from the ψ-shifted Dirac equation; and (§7) the Born rule from the Petersson inner product on mock modular forms. Each section carries a rigour classification following the MEF convention: Rigorous (theorem-level), Derived (calculational chain with stated assumptions), Motivated (physical argument with identified gaps), or Gap (open problem).