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TITLE:
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Universal Threshold Field Theory v1.1: Field Type Classification and β-Heterogeneity as Diagnostic Parameter


AUTHORS:
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Johann Römer
(Add co-authors if applicable)


PRIMARY CATEGORY:
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physics.data-an (Data Analysis, Statistics and Probability)


CROSS-LIST CATEGORIES:
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nlin.AO (Adaptation and Self-Organizing Systems)
physics.ao-ph (Atmospheric and Oceanic Physics)
cs.AI (Artificial Intelligence)
q-bio.PE (Quantitative Biology - Populations and Evolution)


ABSTRACT:
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The Universal Threshold Field (UTAC) framework models emergent transitions across complex systems using a logistic quartet (R, Θ, β, ζ(R)), where β represents transition steepness. We present an extended empirical analysis (n=15 domains spanning astrophysics, climate, biology, and AI) revealing systematic β-heterogeneity (range: 2.50-16.28). Rather than representing methodological artifacts, this heterogeneity reflects fundamental differences in system architecture. We introduce a field type classification framework based on coupling strength, dimensionality, coherence, memory, and threshold dynamics. One-way ANOVA demonstrates that field type explains 68% of β-variance (F=10.9, p=0.0025, η²=0.680), identifying four distinct regimes: (I) Strongly Coupled (β=4.44±0.73), (II) High-Dimensional (β=3.63±0.25), (III) Weakly Coupled (β=2.50), and (IV) Physically Constrained (β=12.05±5.90). Type IV systems (black holes, urban heat islands, Amazon moisture retention) exhibit near-discontinuous transitions (β>10) resulting from low dimensionality combined with extreme coupling. Simulation validation (80 parameter sweeps) confirms coupling × dimensionality interactions generate β-heterogeneity. These results transform β from a purported universal constant into a diagnostic parameter revealing system architecture. Code, data, and full reproducible analysis: https://github.com/GenesisAeon/Feldtheorie (DOI: 10.5281/zenodo.17472834).


COMMENTS:
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40 pages, 4 figures, 5 tables. Field type ANOVA explains 68% of β-variance (p=0.0025). Full reproducible code and data at GitHub/Zenodo (DOI: 10.5281/zenodo.17472834)


LICENSE:
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Creative Commons Attribution 4.0 International (CC BY 4.0)
OR
arXiv's default non-exclusive license

Recommendation: CC BY 4.0 for maximum openness


MSC CLASSES (optional):
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37N20 (Dynamical systems in other branches of physics)
86A08 (Climate science and meteorology)
92D25 (Population dynamics)


KEYWORDS (optional):
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threshold dynamics, field type classification, system architecture, tipping points, β-heterogeneity, logistic response, climate transitions, AI emergence, ANOVA, diagnostic parameter


ACM CLASSES (for cs.AI):
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I.2.0 (Artificial Intelligence - General)
J.2 (Physical Sciences and Engineering)


NOTES:
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- First submission to arXiv
- Endorsement may be required for nlin.CD
- Code and data fully open at Zenodo DOI: 10.5281/zenodo.17472834
- Contact: [your email]
