Hybrid Odd-Prime Router

The opening sentence sets the tone for the whole document: a complete strong-BSD family does not require a single theorem to cover all $p$. The document formally consolidates all the tools accumulated in documents 00-11 into a six-class routing table: P0 ($p=2$, directly using Banwait–Huang Theorem 2.14), P1 (support primes where $p\mid d$, requiring $p\ge5$, good ordinary, residual irreducibility, and having a multiplicative residual-ramification witness, using existing additive-twist ordinary theorems), P2 (good ordinary and $p\nmid d$, branching by residual reducible/irreducible to use reducible/Eisenstein ordinary theorems or ordinary Iwasawa theorem/BCS, **explicitly not using FW**), P3 (fixed multiplicative $p\mid N$, finite set checked prime by prime), P4 (fixed additive $p\mid N$, finite set, this is where FW's H1/H2/H3 plus Manin compatibility are truly used), P5 (good supersingular, applying the derived FW bridge from document 11, H1/H2 automatic, H3 given uniformly by $g_-(E)$). The document concludes the effect of the entire routing strategy in one sentence: the original $\forall p>2$ is split into four blocks—a finite bad-prime table, support-prime restrictions, ordinary theorems, and a supersingular uniform certificate—the document explicitly points out that this is the viable global quantifier compression, rather than forcing a single framework to handle all cases.