MCIR Topologies

The representational topology of an intermediate representation is not a neutral storage choice. It determines which relations are local or shared, which structures can be reused, how scope is expressed, whether cycles are possible, how history is retained, which proofs are tractable, and which changes can be made without silent semantic loss. For MCIR, topology is therefore constitutional. This paper develops the design space opened by that claim. AST and DAG are not two exhaustive alternatives. A tree is itself a restricted directed acyclic graph, while typing, layering, hyperedges, state-transition semantics, temporal versioning, constraint overlays, and authoring/canonical duality are partly orthogonal dimensions. The paper reorganizes the source taxonomy around a topology profile rather than a flat list of competing structures. The strongest candidate architecture is a coordinated representational family: a scoped tree with references for authoring and local containment; a typed graph for canonical sharing and dependency; a separate receipt-lineage graph for provenance and decision history; and explicit projections into workflow, constraint, temporal, and visualization views. This is a design candidate, not an adjudicated MCIR identity or implementation. Multiple representations create their own constitutional burden. Each projection must state what it preserves, what it omits, whether round-tripping is permitted, how identity is maintained, and which representation is authoritative for each claim. Without those contracts, a multi-topology architecture can increase semantic drift rather than reduce it. The result is a specification and evaluation framework for choosing MCIR configurations through CM1 and CM2, selecting an Instance Constitution or Instance Configuration, and eventually producing an Instance Realization or Implementation Realization with evidence. No implementation or canonical standing is asserted.