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

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.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-03-20
DOI
https://doi.org/10.5281/zenodo.19123673
Primary Topic
Formal Methods in Verification
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

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

Andrew John Paton
Zenodo (CERN European Organization for Nuclear Research)
Formal Methods in Verification
article

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

Andrew John Paton
article en

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.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 13%
Formal Methods in Verification
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.