A mathematical theory of redox biology.

Redox biology is commonly described through functional labels, such as oxidant, reductant, antioxidant, signalling mediator or damage mediator. However, these labels do not define invariant molecular properties. A molecule may realize different functions depending on reaction partner, local coupling, spatial domain and prior trajectory. Function is therefore not primitive but emergent. Here, we develop a mathematical theory of redox biology from first principles. At the mesoscopic level, chemically defined molecular states are treated as objects and reactions as transformations, yielding an admissible biochemical state space naturally represented as a hypergraph. Function is then defined as a derived relational quantity induced by realized flux over this structural network. As realized flux is temporally mutable, function is necessarily dynamic. By introducing locality, the realized redox state is mathematically represented as an informational occupancy field over space and time. This field is bounded, admits geometric deformation and provides a formal basis for memory, attractors and coarse-grained scalar descriptions like oxidative stress. Measurement and manipulation are treated as coupled informational interfaces to this field, bounding causal inference. The theory yields falsifiable predictions, including flux-dependent function at fixed concentration and history-dependent responses under matched present inputs.