Aggregation Irreversibility in Traceability Systems

Traceability is often treated as a technological problem or as a matter of implementing information systems. However, fundamental limits exist that do not depend on technology but on the structure of the available information. This work establishes the principle of aggregation irreversibility, according to which aggregated information cannot be used to reconstruct the original contributions if these were not recorded at the moment of transformation. It is shown that when materials or quantities are recorded only as aggregated totals, the later reconstruction of causal relationships between lots and lot fractions becomes logically impossible. This limit cannot be overcome by technological means alone, regardless of computing capacity, analytical tools, or investment. The principle explains why many systems that record inventories and quantities fail to provide real traceability, particularly in production and transformation environments where materials are physically combined and modified through the use of lot fractions originating from multiple input lots. Traceability must therefore be understood as the preservation of causal information at the moment of transformation. Information not recorded at that moment is irreversibly lost.