AdaptoFlux: A Typed Graph Representation Substrate for Stateful Symbolic Program Synthesis

Discrete program synthesis searches a combinatorial space of typed, executable structures, where invalid operator compositions and state-dependent control logic make even well-formed programs hard to discover. We present AdaptoFlux, a representation substrate that couples a metadata-driven Method Pool—registering heterogeneous, typed operations, including side-effectful actions—with Generalized Data Flow Graphs (GDFGs), typed DAGs whose edges are statically checked for type compatibility. State-dependent behavior is accommodated without abandoning the DAG formulation: through time-step unrolling, nodes read from and write to an implicit external state, decoupling mutable state from graph topology. AdaptoFlux deliberately separates the representation space from the search procedure: type constraints prune invalid compositions before search begins, and the same substrate can be paired with arbitrary optimizers. Using lightweight gradient-free search procedures as proof-of-concept probes, we validate the space's navigability, type safety, and interface completeness on canonical static tasks; on a minimal stateful synthesis task, the type-constrained space automatically synthesizes the target stateful graph in 8 of 10 runs, versus 0 of 10 when type routing is disabled. A hand-crafted GDFG controlling a Snake agent further demonstrates that pure computation and side-effecting actions can execute within a single unified graph. AdaptoFlux is a concept-and-feasibility contribution to representation design, not a new optimization algorithm, and is not intended to outperform specialized symbolic-regression systems (e.g., PySR, gplearn) on static benchmarks.