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This paper aims to address the two-variable Jacobian conjecture, focusing on the degree pair (72,108) and its associated computational challenges.

August 3, 2026Open Access

A planar program for the two-variable Jacobian conjecture: a theorem ladder, staircase transport, and machine certificates at the (72,108) frontier

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Randomized trial investigates exact arithmetic solutions for the two-variable Jacobian conjecture, suggesting new pathways for resolution.

This paper aims to address the two-variable Jacobian conjecture, focusing on the degree pair (72,108) and its associated computational challenges.
Developed an exact-arithmetic campaign for the degree pair (72,108)
Constructed a complete declared four-coefficient restriction with a first transverse boundary theorem
Generated maximal minors from an augmented matrix to establish a unit ideal.
Derived normalized determinants P, Q, R associated with maximal minors
Closed the complete direct boundary for the five-coefficient restriction
Identified remaining challenges related to nonzero lifts and transverse quotients.

Felipe Santibañez-Leal (2026) studied this question.

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Randomized trial investigates exact arithmetic solutions for the two-variable Jacobian conjecture, suggesting new pathways for resolution.