Empirical Symmetry as a Relational Phenomenon: Informational Linkage Gaps and Agent-Relative Irreducibility

We develop and defend the thesis that a significant class of empirical symmetries — situations in which finite agents cannot discriminate between competing hypotheses — are better understood as relational phenomena emerging from the interaction between the domain’s informational structure and the agent’s extraction capacity, rather than as intrinsic properties of the world. The central mechanism we identify and analyze is the informational linkage gap: the absence, for a given class of agents, of any operationally accessible procedure connecting the agent to the discriminating information. This differs from mere resource limitation: even with sufficient budget, an agent without a procedure to direct search cannot reliably reach the discriminating information. We further identify recursive linkage gaps, in which closing one gap reveals a subordinate gap, creating hierarchical irreducibility. The framework proposes a fourth category of uncertainty — agent-relative irreducibility — that we argue sits between contingent ignorance and structural impossibility and is not adequately captured by existing accounts. Empirical support comes from a computational experiment on 3-SAT backbone structure; historical support from systematic cross-domain connection gaps in the history of science. The central thesis we develop is: Some empirical symmetries are relational phenomena that emerge when discriminating information, though present in the domain, is not accessible through any effective procedure for the class of agents under consideration.