The Informational Basis of Social Choice under Model Uncertainty: Transparency, Robustness, and a Social-Choice Nyquist Limit

central falsification. We prove that the entire class of regulatory interventions based on making strategic manipulation costly---compliance burdens, switching penalties, retraining costs, bureaucratic friction of any magnitude---is provably useless against a competent adversary in transparent institutional regimes. The reason is geometric: the optimal attack on institutional inference requires no movement at all. This friction irrelevance principle directly falsifies a foundational assumption of regulatory policy. We further prove that friction can be actively counterproductive: when it constrains the auditor's ability to switch evaluation metrics, it reduces the institution's verification capacity without reducing the adversary's obfuscation capacity, moving the system toward the failure regime. framework. These results emerge from a general theory of social choice under frame uncertainty when a strategic actor can shape, filter, or distort public evidence. Institutional admissibility is encoded as pairwise -fields Gₗₘ A restricting the information usable to decide a pair (x, y). Under spurious unanimity (Mongin, 1997), expressed unanimity can coexist with latent frame disagreement. We define two governing constants: the pairwise witness capacityW (x, y): =₅ ₅䂲, \ ₆ ₅㶆 C (pf, pg), intrinsic statistical separation of frame-conditioned evidence, and an obfuscation capacity CS bounding the actor's feasible reverse-KL shifts. We prove a sharp aliasing boundary (a ``Nyquist limit''): if CS CW (x, y), the robust Chernoff separation can be driven to zero and a minimax constant misranking floor holds for any decision rule and any sample size. If CS 6 produces 100\% accuracy under a classification incentive and 50\% (chance) under a reward-hacking incentive. The threat is not powerful optimizers generically, but powerful optimizers whose objective incentivizes sycophancy. invariance and friction irrelevance. We replace the static KL budget with a dynamic, state-dependent model with ergodic KL constraint CS^erg. A concavity--convexity chain proves that time-sharing obfuscation strategies cannot outperform the static Chernoff-center strategy; the dynamic boundary equals the static boundary exactly. Since the optimal aliasing strategy (the constant Chernoff center) requires zero switches, switching-cost frictions of any magnitude do not alter the boundary. We strengthen this to a friction counterproductivity theorem: when the auditor faces probe-switching costs, the effective witness capacity CW^fric is strictly reduced, so friction on the auditor side actively helps the adversary. Nyquist processes. We embed the Nyquist boundary in a stochastic game where the witness capacity CW (t) and obfuscation capacity CS (t) evolve as coupled It\ᵒ diffusions driven by technological change, institutional decay, and strategic investment. The Nyquist gap process Z (t): =CW (t) -CS (t) is a one-dimensional diffusion whose sign governs the instantaneous aliasing/recovery regime. We prove: (i) the regime-transition time (the first passage of Z to zero) has an explicit Laplace transform determined by the gap's drift and volatility; (ii) an institutional half-life formula gives the expected duration of recovery regimes in terms of the gap's scale function; (iii) a capacity volatility amplification theorem shows that institutions ``safe on average'' ( (t) >0 for all t) can spend a substantial fraction of time in the aliasing regime if the capacity ratio is volatile; (iv) a survival probability satisfying a Kolmogorov backward equation provides a computable institutional fragility index. This transforms the static inequality CW>CS into a dynamic law of institutional evolution. . Sequential controlled auditing yields an auditing capacity region. A cycle-Nyquist condition governs global aggregation under transitivity constraints. A diagonal-intersection criterion characterizes aliasing under coupling constraints (linear for convex libraries, NP-complete for discrete mixtures). A metric-free Nyquist theorem proves the phase transition persists for every Csisz\'ar f-divergence. A Geodesic Nyquist Theorem on the dually flat statistical manifold identifies the Chernoff center as the e-geodesic equidistance point and unifies all boundaries as -geodesic ball intersection conditions. The framework extends to Markov-dependent evidence, partial observability (with a data-processing inequality reducing CW), and infinite-dimensional manifolds (Gaussian Nyquist boundary). A Nyquist impossibility for mechanism design proves that in the aliasing regime, no incentive-compatible mechanism---even with unrestricted monetary transfers---can elicit truthful frame reports. We formally subsume all four modes of Goodhart's Law as special cases. . Monte Carlo simulations confirm all predicted phenomena: the sharp phase transition, exponential decay versus constant floor, static--dynamic equivalence, both directions of the Nyquist boundary in RLHF, and forensic KS diagnostics detecting aliasing onset with p < 10^-10.