Task-Relative Information Contracts: Sufficiency, Evidence, and Hierarchical Preservation in Multi-Agent Systems

Systems know more internally than they need to expose

Multi-agent systems often know more internally than they need to expose. This paper asks what information must cross an interface if a named receiving criterion is to remain fully usable downstream. It calls such an interface a task-relative information contract, or TRI contract.

For raw state X and candidate contract T = t(X), the TRI deficit measures how much information about the criterion Y is lost at the interface:

Zero deficit means that the full posterior P(Y | X) is preserved.

Four results, one framework

The TRI Contract Theorem identifies the smallest deterministic contract that loses none of this information. In finite discrete systems, that contract also has minimum entropy among deterministic zero-deficit contracts.

In a distributed protocol, the total TRI deficit separates exactly into information lost during reporting and information lost during aggregation.

A separate finite-evidence result shows that finer representations can require more distinctions than the available observations can support, producing a resolution–evidence band under nested refinement. The same finite-evidence structure appears independently in categorical allocation and verification, and reappears when a one-bit evaluation hierarchy is used to attribute learned routing preferences at multiple levels, although the two systems solve different problems.

Conservative internal refinement can also add structure while preserving the same parent-facing TRI contract.

The resulting framework separates what a criterion requires, where a protocol can lose it, what resolution the evidence can support, and when the same external contract survives internal composition.

What the paper does and does not claim

The contract is defined relative to a named receiving criterion. A contract with zero deficit for one criterion can lose information needed by another. The entropy-minimality statement is for finite discrete systems and deterministic contracts.

The finite-evidence result bounds what resolution the available observations can support. It does not supply a procedure for learning a contract from data.

Place in Coordination Information Theory

This paper and Task-Sufficient Contraction came first and do not use the name. The later Recursive Coordination Information Theory paper named their common framework Coordination Information Theory (CIT) and extended it to recursive settings.

The finite-evidence structure here was first met in the allocation and verification paper, and the one-bit evaluation hierarchy is the subject of the hierarchical component selection paper. Those are separate results on separate problems, and this paper records where the same structure reappears.