Exclusion of the (75, 125) Degree Pair in the Plane Jacobian Conjecture

The published candidate census for the plane Jacobian conjecture has a unique configuration of maximum degree exactly 125: the family-F2 degree pair (75, 125). We give an exact computer-assisted exclusion of this configuration. The inner-polynomial theorem of Lee and Li reduces the innermost remainder to twelve possible northeastern vertices. Two vertices are removed by the innermost normalization, two by a final-edge Taylor argument, five by exact quadratic and cubic terms of the ordinary Magnus formula, and the remaining three by a new local Newton–Magnus argument at the quadratic factor z2 − 3z + 3. In the last step, an etale formal coordinate turns every surviving top kernel into a perturbation A3 +βAvr +· · · , where 2 r 8 and β 6= 0. An exhaustive two-case Newton analysis produces an uncancellable negative power of A by Magnus index at most 28, within the published range μ 35. The finite algebra is checked by two implementations, one of which uses only rational arithmetic and an independent polynomial parser. The complete 24-stage audit has a disjoint, exhaustive partition of all twelve vertices. Combined with the cited candidate census and the preceding exclusion at the bound 108, the result advances the integral maximum-degree lower bound from 125 to 126.