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/tests/test_factor_correlation.py

@@ -0,0 +1,105 @@
+"""C1 因子相关性分析测试：横截面 Spearman 相关矩阵（对角线=1、正/负相关符号）。"""
+
+from __future__ import annotations
+
+from datetime import date
+
+import numpy as np
+import pandas as pd
+import pytest
+from app.api import deps
+from app.infrastructure.persistence.sqlalchemy.base import Base
+from app.infrastructure.persistence.sqlalchemy.repositories.market_impl import (
+    SqlAlchemyDailyBarRepository,
+    SqlAlchemyStockRepository,
+)
+from app.main import app
+from app.quant.evaluation import factor_correlation_report
+from fastapi.testclient import TestClient
+from sqlalchemy import create_engine
+from sqlalchemy.orm import sessionmaker
+
+from conftest_quant import bars_dataframe_to_daily_bars, synthetic_daily
+
+_SYMS = ["60000" + str(i) + ".SH" for i in range(5)]
+
+
+def _panel(dates, symbols, drift) -> pd.DataFrame:
+    rng = np.random.default_rng(7)
+    arr = np.zeros((len(dates), len(symbols)))
+    for j in range(len(symbols)):
+        base = np.cumsum(rng.normal(0, 0.5, len(dates)))
+        arr[:, j] = base + drift * np.arange(len(dates)) / 100
+    return pd.DataFrame(arr, index=dates, columns=symbols)
+
+
+class TestCorrelationReportUnit:
+    def test_diag_and_sign(self) -> None:
+        dates = pd.bdate_range("2024-01-01", periods=120)
+        pa = _panel(dates, _SYMS, 2.0)
+        pb = pa * 0.98 + 0.2  # 近线性正相关
+        pc = -pa  # 完全负相关
+        rep = factor_correlation_report({"a": pa, "b": pb, "c": pc}, min_symbols=3)
+        assert rep.factors == ["a", "b", "c"]
+        assert rep.corr_matrix["a"]["a"] == 1.0
+        assert rep.corr_matrix["a"]["b"] > 0.9
+        assert rep.corr_matrix["a"]["c"] < -0.9
+        # 对称
+        assert abs(rep.corr_matrix["a"]["b"] - rep.corr_matrix["b"]["a"]) < 1e-3
+        assert rep.sample_days == 120
+
+    def test_no_common_dates(self) -> None:
+        d1 = pd.bdate_range("2024-01-01", periods=10)
+        d2 = pd.bdate_range("2023-01-01", periods=10)
+        rep = factor_correlation_report(
+            {"x": _panel(d1, _SYMS, 0), "y": _panel(d2, _SYMS, 0)}
+        )
+        assert rep.sample_days == 0 and rep.corr_matrix["x"]["y"] == 0.0
+
+
+class TestCorrelationApi:
+    @pytest.fixture()
+    def client(self, tmp_path):
+        engine = create_engine(f"sqlite:///{tmp_path / 'corr.db'}", future=True)
+        Base.metadata.create_all(engine)
+        Session = sessionmaker(bind=engine, expire_on_commit=False)
+        df = synthetic_daily({s: 0.004 - 0.001 * i for i, s in enumerate(_SYMS)}, n=320)
+        with Session() as session:
+            SqlAlchemyStockRepository(session).upsert_many(
+                [
+                    __import__("app.domain.entities.market", fromlist=["Stock"]).Stock(
+                        symbol=s, name=f"测试{i}", list_date=date(1999, 1, 1)
+                    )
+                    for i, s in enumerate(_SYMS)
+                ]
+            )
+            SqlAlchemyDailyBarRepository(session).upsert_many(bars_dataframe_to_daily_bars(df))
+            session.commit()
+
+        def _override():
+            with Session() as s:
+                yield s
+
+        app.dependency_overrides[deps.get_session] = _override
+        with TestClient(app) as c:
+            yield c
+        app.dependency_overrides.clear()
+
+    def test_factor_correlations(self, client) -> None:
+        resp = client.post(
+            "/api/factor-correlations",
+            json={
+                "universe": {"exclude_st": False, "min_listing_days": 0},
+                "factors": [
+                    {"name": "momentum_20", "weight": 1},
+                    {"name": "momentum_60", "weight": 1},
+                    {"name": "volatility_60", "weight": 1},
+                ],
+                "period": ["2024-03-01", "2024-12-31"],
+            },
+        )
+        assert resp.status_code == 200
+        body = resp.json()
+        assert len(body["factors"]) == 3
+        assert body["corr_matrix"]["momentum_20"]["momentum_20"] == 1.0
+        assert "momentum_60" in body["corr_matrix"]