Phase 2 Global Enclosure Consensus

The opening ruling document for Phase 2, playing a role corresponding to the Global Enclosure of Phase 0, but narrowing the scope to "non-semistable curves"—an area not covered by the Banwait–Huang method itself. The document first cuts three candidate mainlines: higher $2$-power descent, while generally important, is sidelined because Banwait–Huang Remark 2.19 already points out that all LMFDB curves that actually reach the final check_BSD_at_2 in Algorithm 1 have $\operatorname{ord}_2(\#\Sha_{\rm an})=0$; a positive $v_2(\Sha_{\rm an})$ simply hasn't appeared in the current 500K frontier, ruled HOLD / TOOLBOX ONLY. Full rational $2$-torsion ($E(\mathbb Q)[2]\cong(\mathbb Z/2)^2$) is valuable but lacks a corresponding general strong-BSD family theorem version, ruled HOLD. Analytic rank 1 is ruled YELLOW, not the first engineering task, because Banwait–Huang themselves admit that (Im)-class residual-image conditions are difficult to determine algorithmically. The true structural limitation is semistability itself—Banwait–Huang Remark 2.10 directly calls it "a strong restriction", whereas Fouquet–Wan can precisely handle arbitrary reduction type at $p$, except their residual hypotheses have not yet been algorithmised. The document writes the main problem of Phase 2 as a precise implication: $\mathrm{BH2}(E,d)+\forall p>2\,\mathrm{FW}(E_d,p)\Longrightarrow\mathrm{BSD}(E_d)$, and honestly points out that the real difficulty is not "most $p$ are good" or "all $p\le B$ are good", but the quantifier itself—$\forall p>2$—which requires finding a finite exceptional-prime reduction, otherwise one can only admit that this route yields a "$p$-part theorem for a fixed finite prime set". Final ruling: GO into the Fouquet–Wan Hypothesis Compiler, STOP directly attacking the higher 2-descent mainline, HOLD full 2-torsion and rank 1.