The Precision Model: Discrete Planck-Scale Integration and the Universal Information Bound

This paper proposes a shift from the traditional continuous calculus model to a hardware-constrained discrete summation model. By replacing the theoretical differential (dx) with the physical Planck length (lP), we define the "Precise Area Calculation." Furthermore, the model establishes a universal information limit (Omega), asserting that the information density of any given area is strictly governed by the Holographic Principle and Planck-scale resolution. The model suggests that when the information load of a system exceeds the capacity of the surface area (the Holographic Bound), a local system collapse occurs, manifesting as a gravitational singularity. This approach treats reality not as an infinite continuum, but as a deterministic system with fixed hardware limits.