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This research aims to determine the conditions under which local graph-gauge geometries can be globally realized as meromorphic singularities.

April 16, 2026Open Access

Global Meromorphic Geometrization of Renormalized Tail Hierarchies from Graph-Gauge Atlases: Cech Obstructions, Residue Monodromy, and Finite-Cover Recovery

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This research aims to determine the conditions under which local graph-gauge geometries can be globally realized as meromorphic singularities.
Analyzed the compatible hierarchy on connected positive ray manifolds.
Defined local Gaussian residue densities on graph charts.
Proved the first main theorem about constant multiplier differences on overlaps.
Established conditions for global single-valued meromorphic realization via Cech cohomology.
Developed a quantitative finite-cover detector for reconstructing obstruction cocycles.
The diameter of overlap densities proves they differ by a constant multiplier.
A global single-valued meromorphic realization exists if the class in cohomology vanishes.
Identified that twisted realizations occur when the cocycle class is non-zero.
Developed a method to reconstruct obstructions and their monodromy with high accuracy.

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This work elucidates global meromorphic realizations in positive ray manifolds, indicating potential obstructions.

Mohammad Abu-Ghuwaleh (2026) studied this question.

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