The Marshall Triangle: A Triadic Geometric Framework for Modeling Balance in Complex Systems

This record contains version v1.1.2 of The Marshall Triangle: A Triadic Geometric Framework for Modeling Balance in Complex Systems. The Marshall Triangle is a formal geometric framework for representing balance among three competing system priorities. It uses a midpoint-source triangular construction, a reference Harmony Index, and a Gaussian radial-field visualization model to support interpretation of triadic tradeoffs. Version v1.1.2 is a corrected manuscript release. It removes publisher-template residue from the prior PDF, updates the Data Availability Statement with the Zenodo archival DOI, improves mathematical wording around the Harmony Index and source-influence interpretation, updates the conflict-of-interest disclosure, replaces Figure 1 with a higher-resolution canonical image, and removes hidden MDPI sample-template boilerplate from the source archive. The substantive framework, equations, figures, and scholarly references remain aligned with v1.1.1.

Authors

Institutions

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-27
DOI
https://doi.org/10.5281/zenodo.21614304
Primary Topic
Morphological variations and asymmetry
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

The Marshall Triangle: A Triadic Geometric Framework for Modeling Balance in Complex Systems

Paul Warrington Marshall
Zenodo (CERN European Organization for Nuclear Research)
Morphological variations and asymmetry
preprint

The Marshall Triangle: A Triadic Geometric Framework for Modeling Balance in Complex Systems

Paul Warrington Marshall
preprint en

Abstract

This record contains version v1.1.2 of The Marshall Triangle: A Triadic Geometric Framework for Modeling Balance in Complex Systems. The Marshall Triangle is a formal geometric framework for representing balance among three competing system priorities. It uses a midpoint-source triangular construction, a reference Harmony Index, and a Gaussian radial-field visualization model to support interpretation of triadic tradeoffs. Version v1.1.2 is a corrected manuscript release. It removes publisher-template residue from the prior PDF, updates the Data Availability Statement with the Zenodo archival DOI, improves mathematical wording around the Harmony Index and source-influence interpretation, updates the conflict-of-interest disclosure, replaces Figure 1 with a higher-resolution canonical image, and removes hidden MDPI sample-template boilerplate from the source archive. The substantive framework, equations, figures, and scholarly references remain aligned with v1.1.1.

Zenodo (CERN European Organization for Nuclear Research)
Fidélitas University (CR)
Morphological variations and asymmetry
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.

The Marshall Triangle: A Triadic Geometric Framework for Modeling Balance in Complex Systems — Paul Warrington Marshall · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS