What question did this study set out to answer?

To establish a generalized two-dimensional measure-theoretic framework capable of quantifying spatial asymmetry in discrete planar subsets while maintaining strict affine invariance.

August 20, 2026Open Access

Topological Asymmetry and Affine Invariance of 2D Discrete Sets: A Generalized Measure-Theoretic Framework

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To establish a generalized two-dimensional measure-theoretic framework capable of quantifying spatial asymmetry in discrete planar subsets while maintaining strict affine invariance.
Formalized the 2D Vector Drift Operator and a dimensionless Topologically Invariant Divergence Coefficient derived from one-dimensional topological divergence.
Dynamically bounded the continuous integration domain via subset convex hulls to neutralize SO(2) orthogonal rotation and maintain affine invariance.
Systematically tested the framework across four topological benchmark classes: crystalline grids, stochastic domains, Gaussian primes, and Fibonacci sequences.
Demonstrated deterministic isolation of absolute structural stasis in rigid crystalline grids and non-monotonic chaotic variance in stochastic fields.
Confirmed strict asymptotic equilibrium in Gaussian prime distributions.
Identified an exponential structural singularity occurring within the Fibonacci sequence.

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Implication

Theoretical analysis demonstrates invariant spatial asymmetry quantification across two-dimensional discrete geometric sets, establishing a universal framework for structural analysis.

Cite This Study

Yaroslav Donchenko (2026) studied this question.

synapsesocial.com/papers/6a86b5da8a91293e6a1cd702 https://doi.org/10.5281/zenodo.21998012

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Implication

Theoretical analysis demonstrates invariant spatial asymmetry quantification across two-dimensional discrete geometric sets, establishing a universal framework for structural analysis.

Topological Asymmetry and Affine Invariance of 2D Discrete Sets: A Generalized Measure-Theoretic Framework

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Discussion

Implication

Cite This Study

Topological Asymmetry and Affine Invariance of 2D Discrete Sets: A Generalized Measure-Theoretic Framework

Key Points

Discussion

Implication

Cite This Study

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