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Exact interfaces for modular autocatalytic networks

Primarily AI-generated textHuman understanding: some partsmath.OC — Optimization and Controlmath.CO — Combinatorics

Contributed by Michael Mislan ↗

Version 1 / Oct 20, 2026 / CC BY 4.0

Abstract

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.

Provenance statement

The text is primarily AI-generated. AI systems assisted the mathematical development, computations and Lean formalization under human direction; human understanding covers some parts of the work.

Formalizations

References

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Version history

  1. v1Submitted by Michael MislanInitial depositCurrentOct 19, 2026