What question did this study set out to answer?

The aim is to explore the geometric implications of extreme limits of curvature radius in central projection.

April 14, 2026Open Access

On the Limits of the Curvature Radius in Central Projection — The Cases R → ∞ and R → 0

Key Points

The aim is to explore the geometric implications of extreme limits of curvature radius in central projection.
Analyzed the structural behavior of central projection in limits R → ∞ and R → 0.
Utilized geometric frameworks established in prior work.
Constructed a nested structure of subjective spaces to resolve identified tensions.
Both limits R → ∞ and R → 0 exhibit geometrically regular behavior.
A structural tension was identified between geodesic deviation upper bounds and local curvature.
Proposition 4.1 demonstrates that a nested structure can alleviate this tension.

Abstract

central projection framework established in prior papers 1–3. Both limits R → ∞ and R → 0 are geometrically regular. For R → 0, a structural tension arises between the geodesic deviation upper bound and local curvature. A nested structure of subjective spaces (Proposition 4.1) is shown to be constructible from existing geometric degrees of freedom, resolving this tension within the framework. No physical claims are made.

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Cite This Study

Noriaki Kihara (Sun,) studied this question.

synapsesocial.com/papers/69ddda4de195c95cdefd7b6e https://doi.org/https://doi.org/10.5281/zenodo.19526548

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System Equipment (China)

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