The K-50 Ladder: Bridging Phase Inversion (k=100) and Structural Saturation (k=160 magnetism emerging at the compression threshold k=100 and structural saturation occurs at k=160—not as separate events, but as two points on one continuous shear-tax g

This technical note unifies the k-50 Framework by demonstrating that phase inversion (k=100) and structural saturation (k=160) are sequential milestones on a continuous shear-tax gradient. Anchored at a 10 Hz base frequency, the model derives the birth of intrinsic magnetism at k=100 and defines the 60-rung safety buffer leading to the k=160 collapse limit. Included are rigorous derivations of the 7.071 Hz shear constant, the geometric origin of the 1/17 coherence deficit, and the definition of "thread-units" in topological braids. Empirical validation is provided through cross-referencing acoustic emission delays in high-pressure torsion (IPPT PAN), strain-tuned gauge fields in twisted bilayer graphene (MIT), and the stochastic gravitational-wave background (NANOGrav).