The Kummer-Twist Equivalence, the Canonical Elliptic-Chabauty Cover and Residue Transport, the Canonical-Cover Sieve, and the Canonical Second Elliptic Quotient Identified with the Historical E_−

R13: the quotient gate of R12 and the historical G2E.5 gate f_old = 2 − x on E_0 differ by the Kummer class [x] (trivial after pull-back along the 2-isogeny), merging the two lineages. R14: selects the canonical cover r² = 2 − x on E_0 with odd-index surrogate Q = (1, 961408/950625) (odd index certified mod 17), transports the R11 packet with the torsion ambiguity removed, and gives the canonical genus-2 sextic Y² = (2 − r²)(M²r⁴ − 2M²r² + L²). R15: a finite-prime sieve on the canonical cover at two new primes 11,532,251 and 15,721,883 (projected order 2^19) eliminates no R11 class — a negative (no-progress) computational result, so elliptic / quadratic Chabauty is the next escalation. R16: makes the second quotient explicit and identifies it with the historical integral E_−, so Jac(H_can) ~ E_0 × E_− has rank 2 = g (ordinary Chabauty fails, the quadratic-Chabauty dimension criterion holds); a dual-quotient sieve at the same two primes again eliminates nothing.