This paper formalizes and sharpens Donald Hoffman's interface theory of perception (ITP) by embedding it within the adversarial aggregation channel (AAC) framework. Hoffman's evolutionary game-theoretic argument establishes that natural selection generically favors fitness-tuned over veridical perceptual systems, but leaves three formal gaps: no sharp threshold identifying when non-veridicality is forced, no necessity proof, and no rigorous mechanism for why the perceptual interface is inescapable. The AAC framework supplies all three. A perceptual Nyquist theorem establishes a sharp phase transition governed by the ratio of effective environmental complexity to perceptual bandwidth. In the sub-Nyquist regime — when perceptual bandwidth falls below the number of independent environmental dimensions along which the fitness-optimal action varies — aliasing is forced and fitness-tuned compression generically diverges from veridical representation. In the super-Nyquist regime, veridical perception is not only possible but fitness-optimal. This refines Hoffman's claim from "almost never veridical" to "non-veridical above a precise threshold." A Goodhart subsumption theorem for evolution identifies the formal mechanism: natural selection targets reproductive fitness as a proxy for environmental fit, and once the proxy is targeted by selection, it diverges from truth at a rate governed by the AAC conservation identity. Fitness-equivalent but truth-distinct states are progressively collapsed, and the divergence is self-reinforcing across generations. A perceptual renewal trap theorem proves lock-in: in the sub-Nyquist regime, the fitness-optimal allocation of cognitive bandwidth devotes zero resources to scouting the true environmental structure, because scouting has zero marginal fitness return. The interface is self-confirming — all experience is interpreted through fitness-tuned categories, and no experience contradicts them, because the organism cannot perceive the states the categories alias. A perceptual conservation identity proves that enriching perception through instruments, science, or cognitive enhancement shifts the impossibility but cannot eliminate it: the total information deficit is conserved, enrichments subject to the same selection pressure inherit the fitness-truth divergence, and only fitness-independent enrichments achieve full escape on specific aliased pairs. A scientific escape theorem characterizes the partial exit: instruments expand effective bandwidth and, being designed for truth-tracking rather than reproductive fitness, avoid Goodhart corruption on instrumented domains. The residual impossibility persists on uninstrumented domains, through the biological channel bottleneck on instrument outputs, and through Goodhart pressure on theory selection. A quantum interface theorem provides the deepest result, connecting the perceptual renewal trap to the decoherence renewal trap. Decoherence compresses quantum states to classical pointer states with a Nyquist ratio of 1/(N+1) for an N-dimensional system — always sub-Nyquist and growing worse with system size. The classical perceptual interface is therefore not merely fitness-optimal but physically locked in by decoherence irreversibility, imposing a physical layer of sub-Nyquist compression that no organism or instrument operating in a decohered world can escape. These results place the ITP alongside Arrow's theorem, the Cambridge Capital Controversy, the Triffin Dilemma, and the quantum no-cloning theorem as instances of a single conservation law governing adversarial aggregation channels.
Kevin Fathi (Tue,) studied this question.