Abstract
Embodied agents interacting with the same physical process may maintain heterogeneous, asynchronous, and observer-relative representations. Rather than assuming that such representations should always be globally aligned, we investigate which distinctions among them must actually be resolved for coherent interaction. We formalize this question through relational sufficiency: an interaction-specific relational-evidence map defines the representational ambiguity left unresolved by comparison, and sufficiency holds when each residual ambiguity fiber lies within an interaction-equivalence class. When this condition fails, additional sensorimotor anchors must separate precisely the ambiguities that can change the interaction-relevant outcome. For smooth systems, we derive a local first-order lower bound on the number of inde- pendent scalar anchors required, given by the dimension of directions that are invisible to relational evidence but visible to the interaction-relevant map. We instantiate the theory in two variants of an asynchronous hand-off scenario that share the same observer agents, representations, transports, and relational evidence. Relative synchronization requires no additional anchor, whereas hand-off at an absolute time requires exactly one. The analysis there- fore provides a task-relative stopping condition for representational alignment: residual disagreement need not be eliminated when it is invariant with respect to the interaction.
Abstract (translated)
URL
https://arxiv.org/abs/2610.02985
