Quantitative Analysis of the Equator and Breathing of the Envelope Interface

Within the envelope surface framework, the envelope surface is a three-dimensional perceptual surface formed by the bending and closure of the survey line spiral in a vortex field, and its breathing manifests as periodic expansion and contraction. Based on the uniformly accelerated/decelerated motion model, this paper provides a quantitative analysis of the breathing structure and equator line of the envelope surface. We define the breathing rate as the ratio of the absolute value of acceleration during the accelerated segment to the absolute value of acceleration during the decelerated segment, and prove that the breathing rate is equal to the ratio of the distances from the poles to the equator line. Thereby establishing the quantitative relationship between the breathing structure of the envelope surface and observable physical quantities, providing a mathematical foundation for experimental testing of the envelope surface framework. This paper points out that human theories implicitly assume a breathing rate of 1, i.e., the equator line lies exactly midway between the two poles — an assumption that has never been tested. Keywords: envelope surface, equator line, breathing rate, uniformly accelerated motion, envelope surface breathing structure