The Planck Field: A Mechanical Resolution to Relativistic Infinities and the Singularity Problem - Reconciling the PSR B1913+16 Timing Residuals and the GW170817 Discrepancy

This paper introduces a mechanical refinement of the Metric Field where we identify matter, gravity, and time as constituent components of a Tensor Field. We propose that these constituents are bound by the laws of physics to maintain an internal equilibrium within the field's structural capacity. We demonstrate that as mass density approaches the Planck scale, the field exhibits a saturation-dependent response as an impedance scalar. This creates a physical "floor" of geometric rigidity—a maximum structural threshold—that prevents the formation of singularities without requiring a redefinition of the gravitational constant G. Instead, the field's displacement reaches an asymptotic limit equal to Planck's density, precluding infinite density. We evaluate this framework against the Hulse-Taylor Binary (PSR B1913+16) timing residuals, demonstrating that the observed "lag" correlates with the field’s transition toward this rigidity. This model provides a more precise alignment with forty years of observational data by accounting for the field's internal resistance to extreme matter loading. We further evaluate the framework against the GW170817 discrepancy demonstating the effect on the speed of propagation due to the induced scalar impedance of the Tensor (Planck) field.