Semiotics of the Numbers 45 and 506: From f(x) = -x^2 + 45x + 1/4 to the Logistic Ceiling of 45.01 Thousand Sq Miles, the 506th Regiment, and Russia's 46 Thousand Sq Miles Wall in Ukraine

This journal shows semiotically that the numbers from the quadratic function f(x) = -x² + 45x + 1/4, namely b = 45, D = 2026, b^2 = 2025, axis of symmetry 22.5, vertex 506.5, and distance between intercepts 45.01, are consistently used in the logistic function f(t) = 45.01 - 90 / (1 + e^{22.5(t-2025)}). The number 90 comes from the integral from 0 to 45 of (-2x + 90) dx = 2025, a triangle with base 45 and height 90. The vertex 506.5 is interpreted semiotically as 506 + 0.5, where 506 is the 506th Motor Rifle Regiment of the Russian Group of Forces "Centr", and 0.5 is the half-step across the administrative border. After Russia obtained 45 thousand sq miles, Russia never broke through 46 thousand sq miles, consistent with the model ceiling of