SDRIS: The Geometric Origin of Uncertainty – Deriving the Heisenberg Limit (Δx·Δp ≥ ħ/2) from the Fourier-Bandwidth Constraints of the Recursive Grid (Series: Paper 105)

The Heisenberg Uncertainty Principle is conventionally interpreted as a fundamental limit of nature's precision or as a consequence of measurement disturbance. In this paper, we propose a structural reinterpretation within the Static-Dynamic Recursive Information Space (SDRIS) framework. We demonstrate that quantum uncertainty is mathematically isomorphic to the Time-Bandwidth Product in signal processing. By modeling the vacuum as a discrete information grid, we identify the uncertainty relation not as an intrinsic indeterminism of the object, but as a Representation Limit arising from the projection of infinite information onto a finite-bandwidth substrate. Key Results: Geometric Derivation: We derive the uncertainty inequality $\sigma_x \sigma_k \ge 1/2$ strictly from the properties of the Fourier Transform on a lattice, identifying the Planck constant $\hbar$ as the scaling parameter converting grid bandwidth into physical momentum ($p = \hbar k$). Numerical Verification: Included Python simulations (FFT) confirm that Gaussian wavepackets minimize the uncertainty product to exactly $0.5$. This proves that "fuzziness" is effectively the compression artifact of a finite-resolution universe. Ontological Shift: The paper recovers the standard quantum mechanical limit while providing a rigorous geometric foundation based on discrete signal theory, removing the need for an axiomatic "indeterminacy principle." Includes: Full mathematical derivation (Fourier Duality). Python Simulation Notebook (102_18116715_SDRIS_Born_Rule_Simulation_Code_v1_0.ipynb) verifying the lower bound.