
We identify a universal functional form governing friction and viscosity transitions across threephysically distinct systems spanning 15 orders of magnitude in velocity. In each case, the critical regime transition — thefriction minimum in bearings, the Newtonian plateau in blood, and the seismogenic zone boundaryon faults — corresponds to the zero-crossing of the continuously varying exponent α + β log x. Thissingle mathematical structure replaces piecewise regime models that have been standard in theirrespective fields for decades. The varying exponent arises naturally from the competition betweentwo power-law rate processes whose relative dominance shifts logarithmically with the state variable.
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