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April 1, 20260 citationsOpen Access

FROM SYSTEM TO DOMAIN Structural Invariance Across Constraint Environments

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APAndrew John Paton

Key Points

  • The central aim is to formalize how the Paton System operates across different domains under constraint.
  • Defined the relationship between the Paton System and specific domains.
  • Examined the effects of varying constraints on system behavior.
  • Developed a unified framework for cross-domain interpretation.
  • Identified invariance in structural logic across diverse domains like physics, biology, and computation.
  • Demonstrated that structural behavior is consistent despite different constraints.
  • Clarified that domain theories describe expressions of structure rather than the structure itself.

Abstract

This paper formalises the relationship between the Paton System as a domain-neutral structural framework and its instantiation across specific domains. The Paton System defines the conditions under which systems can exist form and continue under constraint. Domains are defined as systems operating under specific constraint sets. Variation between domains arises from constraint differences rather than structural change. The same invariant structural logic governs all domains. A mapping from system to domain is defined in which observable behaviour emerges from the interaction between the invariant system and domain-specific constraints. This explains why similar structural behaviour appears across physics biology computation and other fields. The paper clarifies that domain theories describe expressions of structure rather than structure itself and establishes a unified basis for cross-domain interpretation.

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Cite This Study

Andrew John Paton (2026) studied this question.

synapsesocial.com/papers/69ccb75916edfba7beb8934chttps://doi.org/10.5281/zenodo.19325727
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