Which Structures Carry Information?: The Causal Structure Set and the Inverse Problem of Heredity
The universe is saturated with statistical dependence and, for most of its history, contained no information carriers at all. Information carriers are configurations that are copied and whose differences cause different structures to be produced. We conjecture that information carriers and hereditary organisation emerge together, and formulate their identification as a joint inverse problem. We introduce the Causal Structure Set (CSS), a finite labelled strict partial order of persistent physical structure instances and their realised causal ancestry. Structural types are established independently of hereditary-role inference. Causally convex subsets define processes with explicit input and output boundaries, within which hereditary motifs can be sought and tested. Our initial criterion combines replication, variation and translation within one candidate family, with lineage continuation. Translation requires variants to act through corresponding operator organisation to produce distinguishable structural types absent from the respective inputs, with the output distinction caused by the variant distinction. A replicated descendant must subsequently re-enter replication. Carrier, operator and product roles are assigned only when this joint organisation is identified; lineage depth measures its realised continuation. We give sufficient conditions for preserving physical witnesses under admissible changes of representation and define cross-substrate correspondence through process boundary organisation. Synthetic and hypothetical examples illustrate its limitations. CSS addresses systems whose hereditary entities are unknown, contested or emergent. The representation accommodates alternative criteria; the present criterion's adequacy and empirical validation remain open.