K-Protocol 4: Digital Resolution and the Geometry of Intuition - Reinterpreting $\pi$ through Decimal Zoom-in ($10^n$) and Infinite Divergence ($\infty$)

This paper (K-Protocol 4 v3) redefines the mathematical constant $\pi$ not as a mere 'result of calculation,' but as an ontological reality of information that manifests according to digital resolution ($10^n$). While traditional methods demand infinite computational labor to approximate irrational numbers, this protocol proposes an "Inverse-Basel Mapping" algorithm. By re-engineering Euler’s Basel Problem ($\sum 1/k^2 = \pi^2/6$) from the perspective of digital resolution, the protocol ensures precise convergence to $\pi$ as the resolution ($n$) increases. Furthermore, to eliminate floating-point errors, we introduce the 27,720 Integer Grid System—the Least Common Multiple (LCM) of integers 1 through 12. This methodology allows for the efficient 'look-up' of irrational approximations within an integer coordinate system, transcending conventional arithmetic and establishing a new technology of "Information Zoom-in." This version (v3) specifically fixes previous convergence issues, providing a stable mathematical framework for zero-error digital computation. ※ Main Theory (GUT) Link: https://doi.org/10.5281/zenodo.18530872 KProtocol3 Link: https://doi.org/10.5281/zenodo.18531713