FW-H3 Exact Elliptic-Curve Compiler

Defines $W_-(E)=\{\ell:\ell\parallel N_E,\ E\text{ nonsplit multiplicative at }\ell\}$, and writes the FW-H3 criterion already refined in document 08 as: $\mathrm{FW\text{-}H3}(E,p)\iff\exists\ell\in W_-(E),\ \ell\ne p,\ p\nmid v_\ell(\Delta_{\min})$. The core contribution of the document is a uniform certificate: let $g_-(E)=\gcd_{\ell\in W_-(E)}v_\ell(\Delta_{\min})$. If $W_-(E)\ne\varnothing$ and $g_-(E)=2^a$ (meaning no odd prime simultaneously divides all witness valuations), then for **all** $p>2$ simultaneously, $\mathrm{FW\text{-}H3}(E,p)=\mathrm{PASS}$ — one only needs to verify a finite base certificate to close H3 for the entire odd prime quantifier all at once. This is the first time in the entire series that the "∀p>2" problem defined in document 04 is truly compressed into a concrete case of finite checking on this single H3 hypothesis, rather than just a theoretical possibility. Finally, the document reiterates twist-family preservation: if the Banwait-style twist family requires every $\ell\mid N$ to split in $\mathbf Q(\sqrt d)$, then the quadratic twist character is trivial on $G_{\mathbf Q_\ell}$, so the same H3 witness is preserved along the entire family — echoing Lemma C of document 03.