This paper computes the first explicit projection in the Quantum Blueprint Formalism. The pre-coherent space is Mₛ = 0, 1³ with three binary distinctions and incompatibilities ω₁₂ = 1. 0, ω₁₃ = 0. 8, ω₂₃ = 0. 6. The background metric g₀ = δᵢⱼ is flat Riemannian (from the Structural Choice). The tension functional Φ = Σ ω²χ (σᵢ) χ (σⱼ) determines the potential. The symplectic form ωI encodes the incompatibility structure. The Witten Laplacian Hw = −Dₛ Δ + Veff is diagonalized numerically on a 40³ grid (Dₛ = 0. 1). Its spectrum is strictly positive (λ₀ = 0. 79, λ₁ = 1. 65, λ₂ = 1. 65, λ₃ = 1. 66, …) despite the raw Hessian of Φ being indefinite at the pointer state (eigenvalues −1. 05, −0. 32, +1. 37). The spectral gap between the first three excited modes (quasi-degenerate at ω ≈ 0. 93) and the fourth mode (ω ≈ 1. 31) selects a natural projection dimension. The projection π₀: ℝ³ → ℝ² is constructed as the restriction to the two lowest excited Witten eigenmodes. It is an explicit 2×3 matrix. The induced Riemannian metric on the target MΘ has eigenvalues 0. 49, 1. 52 (positive definite). The circulation field Ωₛ, projected onto MΘ, identifies the temporal direction. The signature flip Riemannian → Lorentzian produces gₚhys = diag (−0. 49, +1. 52). The emergent speed of light is c = |Ωₛ|/√Dₛ. This demonstrates, for the first time in the QBF corpus, the complete chain: Mₛ (Riemannian, 3D) → Witten spectrum → spectral gap → projection → induced metric → signature change → MΘ (Lorentzian, 2D). The toy model is 3 → 2 dimensions rather than ∞ → 4, but every structural step is identical to the full theory.
Marcus Schmieke (Fri,) studied this question.