Agency as a Self-Closing Loop: Mutual Surprisal and the Optimization Gap

What is an agent? This paper offers a candidate structural account: agents are systems sustaining mutual surprisal across a self-closing causal loop on its own closure timescale. The account is enumerated rather than universal — RNA, bacteria, Aplysia, and humans are in; thermostats, tornados, and most current LLMs are out — and extended beyond the enumerated cases by a named conjecture (Conjecture A). Universality is not claimed; universality without a state space cannot be cashed. The selection is theory-laden: the four in-cases share other properties (metabolic closure, autopoietic organization, thermodynamic openness) any of which a different framework could elevate. The case for mutual surprisal rests on what follows from it, not on the cases forcing it. What follows is a cross-framework pattern. Reinforcement learning, the free energy principle, predictive coding, active inference, and control theory share a minimization-shape objective whose bare optimum coincides with collapse of mutual surprisal across the loop; their framework-specific machinery performs structurally similar work in preventing the bare optimum. Reward hacking, mode collapse, hallucination, and dark-room dynamics are proposed as slices of this single structural pattern — a reading independently circled by the Proxy Compression Hypothesis (Wang et al., 2026) and the mesa-optimization framework (Hubinger et al., 2019). The operationalization: τ_c is identified with the temporal scale at which dynamical dependence (Barnett and Seth, 2023) across the agent-environment partition is minimized. The identification inherits validated measurement methods from the causal-emergence tradition (Hoel and collaborators). Two named conjectures concentrate the speculative content. Conjecture A (extension): the structural object extends to other systems satisfying the structural conditions. Conjecture B (content-non-selectivity): gap-monitoring oriented at proxy-requirement decoupling cannot be selectively oriented across content domains. A and B carry explicit falsification conditions in the body and are independent. If A holds in the AI direction, a capability-refusal correlation in deployed AI is predicted; if B additionally holds, the correlation is architectural. The AI extension is the most accessible test site for A. The framework is loop-prior and information-first, in the Walker-Davies-Pattee tradition; the contribution is synthetic.