The Geometric Ratio Model – Official Pitch

Official Pitch and Timestamped Disclosure

Title: The Geometric Ratio Model as a structural framework for proportional geometry
Date: May 4, 2025
Author: M.C.M. van Kroonenburgh, MSc (Heerlen, The Netherlands)

Introduction (Pitch)

The Geometric Ratio Model (GRM) introduces a container-first proportional framework for geometric measurement using a fixed structural reference. Rather than treating shapes as isolated objects defined primarily through internal parameters, GRM begins with the frame: a square or cube as the canonical structure against which forms are interpreted.

This approach enables geometric reasoning that is visually interpretable, machine-compatible, and consistent across dimensions. Shapes are evaluated by how they occupy space relative to their enclosing reference, creating a stable basis for comparison and proportional interpretation in both conceptual and applied contexts.

GRM establishes standardized proportional units for perimeter, area, and volume in relation to the square or cube reference frame. These units allow geometry to be interpreted through fixed relational structure rather than parameter-first calculation. The result is a framework that can support clarity in education, consistency in design, and practical integration in digital systems where resolution, sampling, and representation fundamentally influence what can be measured and recognized.

The GRM is designed as a structural complement to classical geometry. It does not replace mathematics, invalidate existing theory, or make superiority claims. Its purpose is to provide an additional proportional layer that improves interpretability and consistency in environments where geometry must be operationalized, implemented, or interpreted digitally.

Why this matters

Many practical systems rely on geometric interpretation, but digital environments introduce constraints that classical geometry does not explicitly address. In imaging, design, CAD workflows, and AI generation, geometry is filtered through discretization, resolution, grids, and sampling. Under these conditions, exact forms become approximated structures, and interpretation becomes sensitive to representation.

GRM introduces a consistent structural reference that allows forms to be compared and interpreted through enclosure and proportion. This supports:

geometry expressed through relation to a reference frame, not internal assumptions
stable container-first logic using the square and cube as canonical structures
proportional interpretation that maps naturally onto digital measurement environments
a clear didactic pathway from structural definition to recognizable form

Scope

GRM is domain-agnostic and supports work in:

mathematics education and conceptual geometry
geometric design and CAD workflows
digital imaging and structure-based interpretation
AI prompting and visual generation with proportional constraints
shape recognition, validation pipelines, and ratio-based measurement concepts

Registration and authorship

This publication serves as an official timestamped disclosure to establish authorship and conceptual precedence of the Geometric Ratio Model (GRM).

Official registration: i-Depot (BOIP) Reference no. 151927 (May 10, 2025).

License and usage

This disclosure text may be shared in unmodified form with attribution. Commercial usage, derivative works, or redistribution of implementation materials requires explicit written permission.

License: Creative Commons Attribution–NonCommercial–NoDerivatives 4.0 International (CC BY-NC-ND 4.0)

Attribution required:
“Geometric Ratio Model (GRM) by M.C.M. van Kroonenburgh, MSc (2025), https://inratios.com“