The PFL-X Symbolic Language: A Minimal Key and Cross-Domain Representation for Admissibility Systems

This paper presents a minimal, user-facing representation of the Pressure-Flow Language Extension (PFL-X), a symbolic system within the Paton System. The objective is to provide a clear, readable, and immediately usable interface for representing system behaviour under constraint. A structured symbolic key and explicit cross-domain examples are provided to demonstrate how input, pressure, evaluation, conflict, and continuation can be expressed without reliance on domain-specific mathematics. The framework encodes system behaviour through a small set of symbols that capture admissibility, overload, conflict, and recovery conditions. The paper is intentionally non-theoretical and does not introduce new formal constructs. Instead, it provides a practical interface layer designed for readability, usability, and direct application across domains including artificial intelligence, economics, biology, cognition, and engineering. The results demonstrate that a common structural pattern governs system behaviour prior to modelling, and that this pattern can be represented in a minimal symbolic form accessible without specialised training. This establishes PFL-X as a domain-neutral, pre-theoretical language for interpreting system behaviour under constraint and enables consistent cross-domain communication of instability, adaptation, and collapse.