feat(factor): M7.1 因子定义入库 + /api/factors 读库（目录契约源）

- factor_definition 表（migration b7f2a5e81c33，MySQL 已应用）：name 主键 + 元数据
  （formula/brief/frequency/lookback/direction/requires JSON/version）+ FactorDefinition
  entity（from_registry_def 由代码注册表构造）
- FactorRepository Protocol + SQLAlchemy 实现（幂等 upsert/list/get）
- /api/factors 改读 DB；目录为空自动 seed 注册表（幂等）—— 保留自定义因子登记能力
  （计算仍须代码注册，引用未注册因子照常 FactorError，防伪因子）
- tests/test_factor_catalog.py（repo 幂等/roundtrip/registry seed、API seed+字段齐全）；
  test_api 的 client fixture 补 tmp sqlite session（factors 读库）；全量 pytest 通过

backend/app/domain/entities/factor.py

@@ -0,0 +1,39 @@
+"""因子目录领域实体（M7.1：因子元数据 DB 化，v2 §11）。
+
+DB 是因子目录的契约源：元数据（含自定义因子登记）入库；
+计算执行仍由代码注册表（quant/factors.py）提供 —— 登记但未注册计算的因子
+在 score/condition 中引用时仍抛 FactorError（防静默伪因子）。
+"""
+
+from __future__ import annotations
+
+from datetime import datetime
+
+from pydantic import BaseModel, Field
+
+
+class FactorDefinition(BaseModel):
+    name: str = Field(min_length=1, max_length=64)
+    description: str = ""
+    formula: str = ""
+    brief: str = ""
+    frequency: str = "daily"
+    lookback: int = 20
+    direction: str = Field(default="higher_is_better", pattern="^(higher_is_better|lower_is_better)$")
+    requires: list[str] = Field(default_factory=list)
+    version: str = "1"
+    created_at: datetime | None = None
+
+    @classmethod
+    def from_registry_def(cls, d) -> FactorDefinition:
+        """由 quant/factors.FactorDef（dataclass）构造目录实体（seed 用）。"""
+        return cls(
+            name=d.name,
+            description=d.description,
+            formula=d.formula,
+            brief=d.brief,
+            frequency=d.frequency,
+            lookback=d.lookback,
+            direction=d.direction,
+            requires=list(d.requires),
+        )

backend/app/domain/repositories/factor.py

@@ -0,0 +1,16 @@
+"""因子目录 Repository Protocol（M7.1）。"""
+
+from __future__ import annotations
+
+from typing import Protocol
+
+from app.domain.entities.factor import FactorDefinition
+
+
+class FactorRepository(Protocol):
+    def upsert_many(self, definitions: list[FactorDefinition]) -> int:
+        """以 name 为幂等键批量写入/更新，返回处理条数。"""
+
+    def list(self) -> list[FactorDefinition]: ...
+
+    def get(self, name: str) -> FactorDefinition | None: ...