  Motivated by the potential connection between metric-affine gravity and
linear Generalized Uncertainty Principle (GUP) in the phase space, we develop a
covariant form of linear GUP and an associated modified Poincar\'e algebra,
which exhibits distinctive behavior, nearing nullity at the minimal length
scale proposed by linear GUP. We use 3-torus geometry to visually represent
linear GUP within a covariant framework. The 3-torus area provides an exact
geometric representation of Bekenstein's universal bound. We depart from
Bousso's approach, which adapts Bekenstein's bound by substituting the
Schwarzschild radius ($r_s$) with the radius ($R$) of the smallest sphere
enclosing the physical system, thereby basing the covariant entropy bound on
the sphere's area. Instead, our revised covariant entropy bound is described by
the area of a 3-torus, determined by both the inner radius $r_s$ and outer
radius $R$ where $r_s\leq R $ due to gravitational stability. This approach
results in a more precise geometric representation of Bekenstein's bound,
notably for larger systems where Bousso's bound is typically much larger than
Bekensetin's universal bound. Furthermore, we derive an equation that turns the
standard uncertainty inequality into an equation when considering the
contribution of the 3-torus covariant entropy bound, suggesting a new avenue of
quantum gravity.
