Ramanujan's Level-11 Quintic Branch: A Dihedral Kummer-Line Map and a Cyclotomic Phase Ideal

A previous Galois–Siegel framework for Ramanujan's prime dissections places the normalized p-th-power radicands arising from the Euler function, φ, and ψ on one cyclic modular-function cover with Galois group (Z/pZ)×/{±1}. A companion preprint made several cubic stages explicit. Here we cross to the first pure quintic case, p = 11, and obtain two complementary descriptions of the same degree-five structure. First, the five actual φ-dissection radicands are connected explicitly, through the binary distribution identity, to Y. Yang's low-height generalized-eta coordinate system on X₁(11). A primitive Hilbert–90 ratio is expressed as a monomial in five Yang conjugates evaluated at τ, 2τ, and 4τ; the relevant exponent orbit has Smith normal form diag(1,1,1,11,0). Second, the standard 5-isogeny X₁(11) → X₀(11) descends on the quotients by negation to a rational degree-five Kummer-line map whose fibre equation is the classical regular D₅ quintic. The modular curve X₀(11) realizes the quadratic subfield of this dihedral splitting field, so base change converts the D₅ cover into the cyclic C₅ modular isogeny. An exact differential identity is also obtained, and the specialization t = 7 yields an irreducible cyclic quintic of discriminant 11⁴, explicitly isomorphic to the maximal real subfield of Q(ζ₁₁). Finally, the 11-primary phase obstruction is reinterpreted cyclotomically. Under the natural identification of the augmentation lattice with Z[ζ₅], the balanced phase-annihilator lattice is the prime ideal (11, ζ₅ − 4), and Yang's exponent selector maps to a principal generator of norm 11. A corresponding phase-ideal statement is proved uniformly for safe primes p = 2ℓ + 1. The individual ingredients are classical; the Ramanujan-specific synthesis and its bibliographic priority have not yet undergone external specialist review.