Explicit Rotation and Arithmetic Obstructions for Null Chains on a Lorentz Ellipsoid

For the ellipsoid x^2/a + y^2/b + z^2/c = 1 in Minkowski space, we compute the positive unreduced rotation lift of the equator return map formed by alternating null geodesics. Put A = 2 integral from 0 to pi/2 of sqrt((a sin^2(t) + b cos^2(t))/(c + a sin^2(t) + b cos^2(t))) dt. A global conformal cylinder and a complementary-period identity give rho = (pi/A - 1)/2. Closure after k equator iterations and r turns is equivalent to A = pi*k/(k + 2*r). Literal tropic-to-tropic chains additionally require an even number of legs. For fixed a,b and a positive target rotation there is exactly one c, with explicit bounds. If a,b,c are positive algebraic numbers with a != b, an application of Wustholz's analytic subgroup theorem to a twice-punctured elliptic curve proves that rho is transcendental, so no chain closes. For a=b, closure is equivalent to sqrt(1+c/a) being rational. Fixed positive rational-rotation loci on a>b>0 are not semialgebraic over the real algebraic numbers and are Zariski dense over the algebraic numbers. GKT's porism, classical generalized-Jacobian theory, Huber-Wustholz and Wustholz's earlier arithmetic announcement are credited. This is an unrefereed, self-audited preprint; no absolute priority or independent or formal verification is claimed.