# 01｜Phase 2 路線矩陣

| Route | 自然輸出 | 全域增益 | 主要 barrier | 裁決 |
|---|---|---:|---|---|
| Higher $2$-power descent | 多處理 positive $v_2(\Sha_{\rm an})$ | current pipeline 幾乎 0 | frontier 中沒有這些 curves | STOP as mainline |
| Non-semistable + existing odd-$p$ patchwork | 部分 non-semistable family | 中 | supersingular / irreducible hypotheses | GO as baseline |
| Fouquet–Wan arbitrary reduction | arbitrary-reduction odd-$p$ BSD | **高** | residual hypotheses algorithmization + $\forall p$ | **PRIMARY GO** |
| BCS ordinary non-semistable | ordinary $p$-part | 中 | non-CM + image hypotheses；不覆蓋所有 reduction types | supporting route |
| Full rational $2$-torsion | 新 $2$-part families | 高潛力 | 缺一般 strong-BSD family theorem | HOLD |
| Analytic rank 1 | rank-1 family BSD | 高潛力 | `(Im)` + 2-part / regulator redesign | HOLD |
| Prime conductor | 新 family | 中 | no spare ramified prime / p=N issues | niche |
| High rank $2+$ | BSD global frontier | 極高 | entirely different theorem layer | separate Phase later |

---

# 主排序

$$
\boxed{
\text{FW non-semistable compiler}
>
\text{full 2-torsion}
>
\text{rank 1}
>
\text{higher 2-descent}
}
$$

這是「對 current Banwait–Huang family theorem 的可擴張性」排序，不是對數學猜想絕對難度排序。