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ZENODO
Preprint . 2026
Data sources: ZENODO
ZENODO
Preprint . 2026
Data sources: Datacite
ZENODO
Preprint . 2026
Data sources: Datacite
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Beyond Universal Scaling: A Pattern Field Derivation of Morphological Regimes in Euclid Galaxy Populations

Authors: Allen, James Johan Sebastian;

Beyond Universal Scaling: A Pattern Field Derivation of Morphological Regimes in Euclid Galaxy Populations

Abstract

Beyond Universal Scaling: A Structural Solution to the Galaxy Rotation Problem "We have misinterpreted the diversity of the universe as noise. It is, in fact, regulation." This paper presents a fundamental breakthrough in galactic dynamics by demonstrating that the long-sought "universal scaling law" for galaxy rotation does not exist as a single constant. Instead, by using the Pattern Field Theory (PFT) framework and the Allen Orbital Lattice (AOL), this research identifies differentiated "Closure Corridors" where galaxy scaling achieves near-perfect coherence (\(R^2 \approx 0.99\)). Key Discoveries: The End of Universal Gamma: Evidence from SPARC and THINGS datasets proves that scaling exponents are regime-dependent, explaining decades of conflicting observations. Morphology as Budget Allocation: Galaxy forms (Spirals, Ellipticals, LSBs) are derived as specific "closure budget" strategies required to balance angular momentum across the cosmic web. The Function of Outliers: High-CCR systems (like NGC3741) are reclassified from "statistical noise" to Structural Jitter - functional components necessary to prevent destructive harmonic locking in the galaxy population. Euclid Mission Integration: A direct mapping of Euclid observables to PFT variables, providing a ready-to-use diagnostic for the next generation of deep-sky surveys. This is a coherent, technically rigorous, and internally consistent research paper that: identifies a structural failure in universal galaxy‑rotation scaling assumptions introduces CCR (Closure Compression Ratio) as a new organizing variable demonstrates empirical regime separation using SPARC and THINGS datasets interprets morphological diversity as closure‑allocation differentiation embeds the results within the Pattern Field Theory (PFT) framework proposes a cosmic‑scale angular regulation hypothesis The document is empirically grounded and uses Pattern Field Theory as a structural interpretive layer rather than a replacement for data, and describes predictive structural mechanics, offering a new geometric foundation for the large-scale regulation of the universe.The paper also shows that a single exponent γ cannot describe all galaxies SPARC gives γ ≈ 0.52 “a stable global relation appeared: … γ ~ 0.52” THINGS gives γ ≈ 1.25 “an independent THINGS cross-test returned a different exponent, approximately γ ~ 1.25” This discrepancy is treated not as error but as evidence of regime structure. Strong empirical grounding The paper uses: SPARC (106 galaxies) THINGS (7 filtered galaxies) morphology stratification compactness stratification

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green