write-solution-section

name	write-solution-section
description	写论文 Solution Method section：线性化策略、Blanchard-Kahn 条件、政策矩阵、求解器精度。当用户说"写解法这一节"、"draft Section 4"时调用。
type	paper-composition

write-solution-section — 解法章节

触发场景

• "写 Solution Method"、"draft Section 4"

输入契约

字段	说明
paper_dir	论文目录
policy_checkpoint	results/checkpoints/<model>_policy.json
numerics_review	quality_reports/<model>_numerics_review_*.md

前置条件

• 政策矩阵 checkpoint validated == true
• numerics-reviewer 通过

步骤清单

Step 1. 子小节结构

1. 4.1 Linearisation / Perturbation Order：解释解法 — 一阶摄动 vs 二阶 vs 投影 vs SSJ。说明为什么选这个（"the model is approximately linear within ±2σ of the steady state"）。
2. 4.2 Stability：Blanchard-Kahn 条件叙述、特征值列出（从 checkpoint 提取）、为什么稳定。
3. 4.3 Implementation Notes（简短一段）：使用的求解器（Dynare / Julia SSJ / 自写 Klein 等），但不贴代码 / 命令。

Step 2. 写法示例

\section{Solution Method}
\label{sec:solution}

The system of equilibrium conditions in Section~\ref{sec:model} is linearised
around the deterministic steady state characterised in
Section~\ref{sec:calibration}. Letting $\hat{x}_t = \log x_t - \log x^\ast$
denote log-deviations from the steady state, the system reduces to a linear
expectational difference equation in the state vector
$(\hat{k}_t, \hat{z}_t)$ and the control $\hat{c}_t$.

The two eigenvalues of the resulting transition matrix are
$\{0.9621,\ 0.9500\}$, both strictly inside the unit circle. The
Blanchard--Kahn condition is therefore satisfied, and the rational-expectations
solution is unique \citep{BlanchardKahn1980}. The policy function for
consumption takes the linear form
\[
  \hat{c}_t = 0.5904\, \hat{k}_t + 0.3228\, \hat{z}_t,
\]
and capital follows
\[
  \hat{k}_{t+1} = 0.9621\, \hat{k}_t + 0.0801\, \hat{z}_t.
\]

The system is solved analytically by the method of undetermined coefficients
\citep{Uhlig1999}, which yields the closed-form policy functions reported
above.  We have verified the analytical solution by independently solving the
generalised Schur form of the system; the two methods agree to machine
precision.

Step 3. 写入 sections/04_solution.tex

Step 4. 评审

paper-reviewer + numerics-reviewer 双审：写作 + 数字一致。

输出契约

• paper/sections/04_solution.tex（约 400–700 词）
• 评审报告

不允许

• 贴代码 / shell 命令（"Run \texttt{python solve_rbc.py}"——不可）
• 写"the pipeline computes" / "the solver returns"——直接陈述结果
• 暴露 checkpoint 文件名

失败回退

症状	处理
BK 条件不满足	阻断，先回到 spec / 校准
数字与 checkpoint 不符	自动从 checkpoint 重读，禁止手抄