Finite Li-Statistic Collisions for Formal Symmetric Zero Multisets

We prove three theorems about the standard Li-type observation of finite symmetric zero multisets, and record two main corollaries. Let H_sym be the class of finite multisets in the open critical strip symmetric under rho -> rho-bar and rho -> 1-rho, and let P(Z) = 1 iff every atom has Re(rho) = 1/2. Theorem A (exact Li collision): for every m >= 1 there exist Z+, Z- in H_sym with P(Z+) = 1, P(Z-) = 0, and identical standard Li observations Li_j(Z+) = Li_j(Z-) for j = 1, ..., m, realised by explicit rational-arithmetic witnesses. Theorem B (no uniform separation): no fixed finite initial segment of standard Li values enforces a strictly positive gap between P = 1 and P = 0 within H_sym. Theorem C (incomparability): the standard Li map O_fin^(K) and the sampled counting map O_theta are incomparable in the information refinement preorder on H_sym. Corollary D (Andersson): agreement with any fixed finite initial collection of Euler factors of the Riemann zeta function does not force a Helson zeta function's zeros to lie on the critical line (existential obstruction pair, using Andersson 2024, Theorem 5 and Corollary 3). Corollary E (joint obstruction): the combined observation O_fin^(K) x O_theta also admits an exact information obstruction. None of these results assume or imply the Riemann Hypothesis. The class H_sym consists of finite formal multisets; the actual zero set of zeta is infinite and subject to additional analytic structure not imposed on H_sym.