One Singularity, One Scale: A Geometric Derivation of Quantum Measurement

Abstract

We present a unified geometric framework in which quantum measurement emerges from the resolved singularity ZZ in quaternionic phase space H². The origin is blown up to the exceptional divisor E ≃ CP³, yielding the tautological bundle O_CP³(−1) whose first Chern class forces the Born exponent k = 1. The global Z₃ symmetry of the genus-3 surface Σ₃ selects the complex structure J and the centralizer U(2) in Sp(2). The optimal discrete regulator is the E₈ lattice, whose 240 roots project to the Witting configuration (40 distinct rays) on CP³. Stochastic holonomy on this divisor fixes the diffusion coefficient exactly to 1, yielding a parameter-free direction-dependent visibility prediction anchored to the QCD flux-tube width. The same bundle restricts to the monopole bundle over the space of measurement axes, forcing spin-1/2 via Berry-phase single-valuedness. The vacuum defect amplitude is identified as the normalized second moment D ≡ G(E₈) ≈ 0.07168. The framework derives Born rule, spin-1/2, and universal visibility from a single resolved singularity and one physical scale. The mapping from D to sin² θ_W remains an open technical step.

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