The K-Kernel Theory: A Unified Non-Markovian Framework for Complex Systems across Physics, Cosmology, and Engineering.

This preprint introduces the K-Kernel Theory, a novel unified mathematical framework based on non-Markovian (non-local) memory dynamics. The central hypothesis is that the "memory" of past states acts as a universal stabilizing force in complex systems, mathematically represented by a convolution integral over the system's history, which acts as a physical safety valve to prevent infinite singularities and numerical instabilities. We present numerical evidence and 2D/3D simulations across five distinct scientific domains, demonstrating the universality of this framework: 1. Cosmology: The memory term prevents the Big Bang singularity (yielding a smooth Cosmic Bounce). Furthermore, the asymmetry in memory decay between matter and antimatter provides a natural mechanism for Baryogenesis (explaining the matter-antimatter asymmetry in the universe).2. Nuclear Engineering: Delayed neutron memory is modeled in a hybrid reactor (Fast + Thermal). The simulation demonstrates that during an emergency shutdown (SCRAM), the neutron flux decays smoothly due to memory effects, preventing catastrophic prompt criticality accidents.3. Computational Electromagnetics: The K-Kernel framework demonstrates strict passivity in Perfectly Matched Layers (PML). Unlike classical CPML models that suffer from spurious reflections and numerical noise at boundaries, the K-Kernel absorbs electromagnetic waves cleanly and without reflection artifacts.4. Quantum Physics: Smoothing attosecond electron dynamics in graphene, eliminating high-frequency numerical noise present in standard instantaneous models.5. Microbiology: Spatial memory driving antibiotic resistance and critical slowing down (CSD) in bacterial populations. The K-Kernel provides a unified perspective on stability and evolution in nature, bridging the gap between quantum mechanics, cosmology, and engineering.