1. W(x) = [[x, i√(1−x²); i√(1−x²), x]] = e^{iφX}（x = cos φ）
2. S(φ) = e^{iφZ} = diag(e^{iφ}, e^{−iφ})
3. U_QSP(Φ; x) = S(Φ₀)·∏_{k=1}^{d} W(x)·S(Φₖ)
4. U_QSP = [[P, i√(1−x²)·Q; i√(1−x²)·Q, P]]，酉性 ⇔ |P|² + (1−x²)|Q|² = 1
5. 可达四条件：deg P ≤ d 奇偶同 d；|P| ≤ 1；|P(±1)| = 1；否则 QSVT
6. T_n(cos θ) = cos nθ、U_n(cos θ) = sin((n+1)θ)/sin θ、递推 f_{n+1} = 2x·f_n − f_{n−1}
7. 全零相位：W^d = [[T_d, i√(1−x²)·U_{d−1}; i√(1−x²)·U_{d−1}, T_d]]
8. 乘积公式 M(P₁,Q₁)·M(P₂,Q₂) = M(P₁P₂ − s²·Q₁Q₂, P₁Q₂ + Q₁P₂)
9. 剥层配平：e^{2iΦ_d} = p_d/q_{d−1}
10. 投影恒等式：(⟨0|^{⊗m} ⊗ I)·Ũ_Φ·(|0⟩^{⊗m} ⊗ I) = P(A/α) = Σⱼ P(σⱼ/α)·|uⱼ⟩⟨vⱼ|
11. 次数界：Jackson d = O(L/ε)；Bernstein ‖f − P_d‖ ≤ 2M·ρ^{1−d}/(ρ−1)；模拟 d = O(τ + log(1/ε))
12. 复杂度账本：模拟 O(αt + log(1/ε))、求逆 O(κ·log(κ/ε))、Grover O(√N)、总门数 O(d·(Ln + C_PREP))
13. 数值侧：切比雪夫节点损失 L(Φ)；确定性构造 O(d) 层剥除、整体 O(d²)；端点挤压相邻相位差 O(ρ^{−d})