Quantum Measurement and Decoherence from the Fibonacci Cascade: Collapse as Cardy Projection

We derive quantum measurement theory from the Fibonacci Cascade Conformal Layer (FCCL). Measurement is identified as a Cardy projection: the probability of obtaining outcome 𝑛 when measuring a cascade state |𝜓⟩ equals |⟨𝑛|𝐵Planck⟩|² = 𝜑^{−2𝑛}/√5 — the Born rule, derived from the Cardy formula without postulation. The preferred “pointer basis” of decoherence consists of the FCCL Cardy boundary states {|𝐵𝑛⟩} — energy eigenstates of the cascade Hamiltonian, selected by the environment because they minimize the cascade free energy. The coherence between cascade levels 𝑛1 and 𝑛2 decays at rate Γ₁₂ = (𝑘_𝐵𝑇 /ℏ) × 𝑁_modes × (1 − 𝜑^{−2|𝑛1−𝑛2|} / √5), recovering standard decoherence scaling for macroscopic objects while protecting quantum coherence for microscopic systems. Quantum Darwinism emerges naturally: the probability that 𝑘 independent environmental modes all record the same measurement outcome is (𝜑^{−2𝑛}/√5)^𝑘 — the Born rule raised to the 𝑘-th power.