Paper 19 - Affinity Geometry, Transfer Laws, and π Invariants in Normalized Binary and Symmetric Multidimensional Exponential Families
Year: 2026
Type: preprint
Abstract: Overview This work develops a clear mathematical framework for studying affinity geometry in binary and symmetric multidimensional systems. It connects several ideas—affinity, Fisher information, transfer laws, and π-based invariants—inside one consistent framework. Main Results The paper provides: an exact relation between affinity response and Fisher information, a Fisher–Rao geometric representation with total length (\pi), balance-count formulas that produce π-related invariants, a faster π estimator using Richardson acceleration, exact transfer laws that convert one affinity value into another, multidimensional Fisher-information formulas, and cross-dimension transfer rules for the stated symmetric family. A key result is that the Fisher–Rao length remains equal to (\pi) for the symmetric multidimensional family studied in the paper. Scientific Scope The paper clearly separates established mathematics—such as Fisher information, Jeffreys priors, Wallis and central-binomial limits, Gudermannian identities, and Richardson extrapolation—from the QDL-specific synthesis built from them. The framework is mathematical. By itself, it does not establish a universal physical law or determine the microscopic physical origin of QDL affinity parameters. In Simple Terms Paper 19 shows how binary and multidimensional affinity can be understood through a common geometric language. It provides exact formulas for moving between systems, comparing dimensions, studying information geometry, and connecting several π-related structures in one reproducible framework. The Zenodo package includes the main manuscript and supporting reproducibility materials, including source files, verification code, theorem audits, metadata, and supplementary material.
Author: chandaliya, Roshankumar
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208821101
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