feat(factor): C1 因子相关性分析（横截面 Spearman 矩阵 + API）

- evaluation.factor_correlation_report：多因子共同日期 ∩ 后逐日横截面 Spearman 相关
  取均值 → FactorCorrelationReport（冗余剔除前置，v3 §12 Correlation→Redundancy）
- ResearchService.run_factor_correlation + POST /api/factor-correlations
  （universe/factors/period；与其它研究同装配口径）
- tests/test_factor_correlation.py：矩阵对角=1/近线性±相关符号/对称/无共同日期补零、
  API 冒烟；全量 pytest 通过

backend/app/quant/evaluation.py

@@ -14,7 +14,7 @@ import math
 
 import pandas as pd
 
-from app.domain.entities.research import FactorTestReport, QuantileReturn
+from app.domain.entities.research import FactorCorrelationReport, FactorTestReport, QuantileReturn
 
 MIN_CROSS_SECTION = 5  # 少于该样本数的日期跳过（避免噪声 IC）
 
@@ -70,6 +70,60 @@ def quantile_returns(factor: pd.DataFrame, forward: pd.DataFrame, quantiles: int
     return pd.Series(means)
 
 
+def _cross_section_corr(pa: pd.Series, pb: pd.Series, min_n: int) -> float | None:
+    """两股票列在某一日期截面值的 Spearman 相关（样本不足 → None）。"""
+    df = pd.concat([pa, pb], axis=1).dropna()
+    if len(df) < min_n or df.iloc[:, 0].nunique() < 2:
+        return None
+    return df.iloc[:, 0].corr(df.iloc[:, 1], method="spearman")
+
+
+def factor_correlation_report(
+    panels: dict[str, pd.DataFrame],
+    *,
+    min_symbols: int = MIN_CROSS_SECTION,
+    max_days: int = 10000,
+) -> FactorCorrelationReport:
+    """两两因子相关：共同日期 ∩ 后，逐日横截面 Spearman 相关取均值。
+
+    用于冗余剔除与因子池管理（v3 §12 流程：Correlation → Redundancy Removal）。
+    """
+    names = list(panels)
+    common = None
+    for panel in panels.values():
+        idx = set(panel.index)
+        common = idx if common is None else (common & idx)
+    if not common:
+        empty = {a: {b: (1.0 if a == b else 0.0) for b in names} for a in names}
+        return FactorCorrelationReport(
+            factors=names, corr_matrix=empty,
+            sample_days=0, sample_min_symbols=min_symbols,
+        )
+    days = sorted(common)[:max_days]
+    corr_matrix: dict[str, dict[str, float]] = {}
+    for a in names:
+        corr_matrix[a] = {}
+        for b in names:
+            if a == b:
+                corr_matrix[a][b] = 1.0
+                continue
+            acc: list[float] = []
+            for day in days:
+                if day not in panels[a].index or day not in panels[b].index:
+                    continue
+                c = _cross_section_corr(panels[a].loc[day], panels[b].loc[day], min_symbols)
+                if c is not None:
+                    acc.append(c)
+            corr_matrix[a][b] = round(float(pd.Series(acc).mean()), 4) if acc else 0.0
+    return FactorCorrelationReport(
+        factors=names,
+        corr_matrix=corr_matrix,
+        sample_days=len(days),
+        sample_min_symbols=min_symbols,
+        config_snapshot={"min_symbols": min_symbols},
+    )
+
+
 def run_factor_test(
     factor: pd.DataFrame,
     forward: pd.DataFrame,

backend/app/quant/service.py

@@ -17,6 +17,7 @@ import pandas as pd
 
 from app.domain.entities.research import (
     BacktestResult,
+    FactorCorrelationReport,
     FactorTestReport,
     ResearchSpec,
 )
@@ -24,7 +25,9 @@ from app.domain.repositories.market import (
     DailyBarRepository,
     StockRepository,
 )
+from app.quant.composite import build_factor_panels
 from app.quant.engine import QuantEngine
+from app.quant.evaluation import factor_correlation_report
 from app.quant.universe import filter_stocks, resolve_members  # noqa: F401 —— 范围过滤
 
 # 流式路径每攒多少行落一个 DataFrame 分片（控制 concat 峰值）
@@ -129,6 +132,12 @@ class ResearchService:
         daily = self._load_daily(spec)
         return self._engine.run_backtest(daily, spec)
 
+    def run_factor_correlation(self, spec: ResearchSpec) -> FactorCorrelationReport:
+        """多因子两两相关（v3 §12）：同 universe/period 装配 → 横截面相关矩阵。"""
+        daily = self._load_daily(spec)
+        panels = {fs.name: build_factor_panels(daily, [fs])[0][1] for fs in spec.factors}
+        return factor_correlation_report(panels)
+
     # ---- 数据装配 ----
 
     def _load_daily(self, spec: ResearchSpec) -> pd.DataFrame: