# 01 | Phase 2 Route Matrix

| Route | Natural Output | Global Gain | Main Barrier | Verdict |
|---|---|---:|---|---|
| Higher $2$-power descent | Handles additional positive $v_2(\Sha_{\rm an})$ | Almost 0 for current pipeline | These curves are not in the frontier | STOP as mainline |
| Non-semistable + existing odd-$p$ patchwork | Partial non-semistable family | Medium | supersingular / irreducible hypotheses | GO as baseline |
| Fouquet–Wan arbitrary reduction | arbitrary-reduction odd-$p$ BSD | **High** | residual hypotheses algorithmization + $\forall p$ | **PRIMARY GO** |
| BCS ordinary non-semistable | ordinary $p$-part | Medium | non-CM + image hypotheses; does not cover all reduction types | supporting route |
| Full rational $2$-torsion | New $2$-part families | High potential | Lacks a general strong-BSD family theorem | HOLD |
| Analytic rank 1 | rank-1 family BSD | High potential | `(Im)` + 2-part / regulator redesign | HOLD |
| Prime conductor | New families | Medium | no spare ramified prime / p=N issues | niche |
| High rank $2+$ | BSD global frontier | Very high | entirely different theorem layer | separate Phase later |

---

# Main Ranking

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

This is a ranking of "extensibility for the current Banwait–Huang family theorem", not a ranking of the absolute difficulty of the mathematical conjectures.