BSD RUGZPB P2/P4 Update: Precise 11-primary Sha closure for 389.a1

Following up on the P1-P7 obligations from document 00, this document tackles P4 (single-prime rank-2 closure) and P2 (whether RUGZPB is just ETNC with a change of sign). The core of P4 is a computation done entirely with integer and finite field arithmetic, containing no floating-point numbers: first, exact row operations are performed over F_11 on the Manin-symbol module of level 389, verifying that the dimension 390-325=65 is exactly equal to 2g(X_0(389))+1; after imposing the Hecke conditions (T_q-a_q)λ=0 for q=2,3,5, the plus involution compresses the target space to exactly one dimension; after fixing λ, it is independently verified that it gives the correct Hecke eigenvalues for all q=2,3,5,7,13,17,19. Next, using ℓ₁=397 and ℓ₂=991 (both satisfying the mod-11 Kolyvagin prime conditions), the Kurihara witness δ₃₉₃₄₂₇⁽λ⁾=6∈F₁₁ is precisely calculated, which is nonzero, and this nonzeroness is invariant under normalization choices. Using Chan-Ho Kim's Theorem 1.8 (an external theorem input, containing no BSD hypotheses) combined with the Mordell-Weil lower bound of rank=2, it deduces ord(δ̃)=2 and Selmer corank=2, and then uses the standard Selmer exact sequence (the rank=corank argument for divisible groups) to strictly prove Sha(E/ℚ)[11^∞]=0—the document specifically performed a "circularity audit" to confirm that the entire reasoning does not presuppose the very finiteness of Sha it aims to prove. The P2 audit concludes that RUGZPB ≠ ETNC (it cannot simply be renamed), but the determinant core genuinely overlaps with the p-TNC/zeta-isomorphism structure; the P1 partial audit finds that local R5 (finiteness of Sha at a fixed prime) can actually be deduced from a strong Selmer structure + exact MW rank, but global R5 remains an independent obligation.