What question did this study set out to answer?

The research aims to develop a normalization framework that maintains geometric properties under transformations.

January 25, 2026Open Access

Rigid Geometric Normalization via an Involutive Map and Hausdorff Convergence

Key Points

The research aims to develop a normalization framework that maintains geometric properties under transformations.
Introduced an axiomatic approach for geometric normalization
Utilized involutive mapping for structural invariance
Employed Hausdorff convergence for consistency in transformations
Provided a framework that preserves geometric consistency under iterative transformations
Demonstrated that the normalization is structurally invariant
Discussed applications to abstract geometric structures

Abstract

This work introduces a rigid geometric normalization framework based on an involutive mapping and Hausdorff convergence. The construction provides a structurally invariant normalization scheme that preserves geometric consistency under iterative transformations. The approach is fully axiomatic and does not rely on empirical calibration. Applications to abstract geometric structures and convergence-controlled normalization processes are discussed.

Rigid Geometric Normalization via an Involutive Map and Hausdorff Convergence

Key Points

Abstract

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