math.OC — Optimization and Control
Exact interfaces for modular autocatalytic networks
We study which information about an autocatalytic reaction network suffices for exact composition with other modules. For the maximum amplification factor, threshold-indexed species-price cones compose by exact set operations, while scalar optima do not. Autocatalytic child-selection cores are reconstructed from complete, uniquely matched ordinary-core anchors using alternating exchange paths and certified rational semipositivity tests. For irreducible unary diluted source networks, positive-composition certificates characterize growth, criticality and extinction under arbitrary species degradation; a related certificate identifies partial-actuation stabilizability. Further manuscript results treat factor interactions, exact boundary traces, contextual indistinguishability and junction-tree composition under running intersection and scope extensionality. Separator width bounds message arity, without a runtime claim. Eleven foundation statements are Palomar registered in Lean 4; the broader historical formalization and conventional extensions retain their separately documented scope. Thermodynamic and passive-tail examples illustrate exact interfaces and information loss. Structural amplification and linear onset conclusions are distinguished from nonlinear kinetic dynamics.