What question did this study set out to answer?

To introduce the Triadic Failure Principle as a model for understanding system breakdown when components are missing.

March 22, 2026Open Access

The Triadic Failure Principle: A Structural Account of System Breakdown Under Missing Components

Key Points

To introduce the Triadic Failure Principle as a model for understanding system breakdown when components are missing.
Introduced the Triadic Failure Principle based on the Triadic Completion Principle.
Defined three irreducible components essential for system validity.
Developed a diagnostic model for predicting failure modes in systems.
Identified specific failure modes corresponding to missing components.
Proposed a structural account of system breakdown applicable across domains.

Abstract

Following the Triadic Completion Principle, which defines the minimal condition for system validity, this paper introduces the Triadic Failure Principle. A system fails structurally when any one of the three irreducible components—potential (♾️), anchor (●), or structure (■)—is absent. Each missing component produces a distinct and predictable failure mode. This framework provides a minimal, domain-neutral diagnostic model for system breakdown, operating prior to modelling, explanation, or optimisation.

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Andrew John Paton

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The Triadic Failure Principle: A Structural Account of System Breakdown Under Missing Components

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