A Minimal Mathematical Framework for Semantic Regeneration

We introduce a minimal mathematical framework in which meaning is treated as a dy-namical object rather than an external interpretation. We define a meaning space as ameasured (pseudo-)metric space, introduce two basic operators (convergent and generative),and formalize a recipe as a finite operator sequence.Under shared initial conditions and operational constraints, we study semantic regener-ation: recovering a meaning trajectory by reapplying a shared recipe without transmittingthe meaning state itself. We emphasize that no semantic content is communicated; only therecipe and the relevant side information (e.g., model choices and parameters) are assumedto be shared in advance. The regenerated state is not required to be identical to the originalone, but is evaluated in terms of structural equivalence.Toy numerical experiments illustrate that regeneration can succeed within this equiva-lence class under shared operational constraints