What question did this study set out to answer?

The aim is to construct and analyze a recursive interval algebra with Omega-weighted metric properties.

March 6, 20260 citationsOpen Access

Metric Geometry of Recursive Interval Algebras over Z^-1: -Weighted Inner Product and Recursive Structure

LZL. P. ZhouSouthwest University of Science and Technology

Key Points

The aim is to construct and analyze a recursive interval algebra with Omega-weighted metric properties.
Developed a recursive interval algebra framework.
Defined an Omega-weighted metric structure with inner product.
Examined canonical refinement and inclusion maps.
Established foundational inequalities and structural properties.
Introduced new insights into the properties of recursive interval algebras.
Demonstrated the utility of the Omega-weighted metric.
Confirmed consistency across recursive depths.

Abstract

This record uploads the preprint RIG-m0: Metric Geometry of Recursive Interval Algebras over (Z^-1). The manuscript constructs and studies a recursive interval algebra equipped with an () -weighted metric structure, including the associated inner product/norm, canonical refinement/inclusion maps across recursive depths, and foundational inequalities and structural properties. Files. RIG-m0. pdf (main manuscript). Status. Preprint (not peer reviewed). An arXiv submission exists and is currently under moderation (“on hold”) ; this Zenodo record provides a stable, citable timestamp. Citation. Please cite the Zenodo DOI of this record. Keywords. Recursive Interval Geometry, -weighted metric geometry, Gevrey structural estimates, Recursive tensor product. Contact. zhoul137@mail. ustc. edu. cn

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