What question did this study set out to answer?

The aim is to develop a framework where meaning is treated as a dynamic object, allowing regeneration of meaning trajectories without direct transfer.

February 14, 2026Open Access

A Minimal Mathematical Framework for Semantic Regeneration

Key Points

The aim is to develop a framework where meaning is treated as a dynamic object, allowing regeneration of meaning trajectories without direct transfer.
Defined a measured pseudo-metric space as a meaning space.
Introduced two basic operators: convergent and generative.
Formalized a recipe as a finite operator sequence to guide regeneration.
Conducted toy numerical experiments to test regeneration under defined constraints.
Successful regeneration of meaning trajectories within the structural equivalence class was achieved.
The regenerated meaning does not need to be identical but must maintain structural equivalence.
Illustrated examples showed effectiveness of the proposed framework under shared operational constraints.

Abstract

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

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