Total Universal Energy as Spatial Volume: A Hypothesis via Katayama Equivalence

This paper proposes that the total mass-energy of the universe (mc²) and the total spatial volume of the universe (4/3πr³) are connected via the Katayama Equivalence (≡ₖ) as different descriptions of the same universe. Version 2 adds Supplementary Material: a Flickr diagram uploaded by the author on July 8, 2010, with the caption 'If a rocket rotates along a circle at the speed of light, it is the size of the universe' — constituting the earliest verifiable public record of the r definition used in this paper, predating the 2026 formalization by 16 years.

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