Open University of Cyprus

Frobenius minimality, minimum-layer uniqueness, and an infinite family of Huneke-Wiegand counterexamples

Son Pham publicly identified the first counterexample to the Huneke-Wiegand conjecture in the class of two-generated monomial ideals over symmetric numerical semigroup rings, subsequently verified independently by Professor Craig Huneke. This preprint preserves that discovery pri...

Curvilinear geometry and primary structure of conductor fiber cones in a Huneke-Wiegand family

For every integer p>=4, a previously constructed symmetric numerical semigroup ring and rigid two-generated monomial ideal determine a conductor ideal whose special fiber is a one-dimensional Cohen-Macaulay algebra of multiplicity 24p. This companion preprint proves the explicit...

Exact replication and screening of tropical finiteness certificates for central configurations

A machine record around Smale's 6th problem (finiteness of planar central configurations of the Newtonian n-body problem). Four contributions, all exact or certified: (i) an exact calibration of the Albouy-Chenciner mutual-distance equations in open tooling, including a machine r...

The bottom of the Shub-Smale tau conjecture: an exact census of integer roots for constant-free straight-line programs of length at most seven

For a univariate integer polynomial f, let tau(f) be the minimum number of +,-,x gates needed to compute f from x and the constants -1,0,1, and let z(f) be its number of distinct integer roots. The Shub-Smale tau conjecture (Smale's fourth problem) asserts z(f) ≤ (1+tau(f))^k for...

The bottom of the Shub-Smale tau conjecture: an exact census of integer roots for constant-free straight-line programs of length at most seven

For a univariate integer polynomial f, let tau(f) be the minimum number of +,-,x gates needed to compute f from x and the constants -1,0,1, and let z(f) be its number of distinct integer roots. The Shub-Smale tau conjecture (Smale's fourth problem) asserts z(f) ≤ (1+tau(f))^k for...

The bottom of the Shub-Smale tau conjecture: an exact census of integer roots for constant-free straight-line programs of length at most seven

For a univariate integer polynomial f, let tau(f) be the minimum number of +,-,x gates needed to compute f from x and the constants -1,0,1, and let z(f) be its number of distinct integer roots. The Shub-Smale tau conjecture (Smale's fourth problem) asserts z(f) ≤ (1+tau(f))^k for...

Frobenius minimality of the Huneke-Wiegand counterexample in symmetric numerical semigroup rings

Son Pham publicly identified a counterexample to the Huneke-Wiegand conjecture in the class of two-generated monomial ideals over symmetric numerical semigroup rings, subsequently verified independently by Professor Craig Huneke. This preprint preserves that discovery priority an...

Frobenius minimality and minimum-layer uniqueness of the Huneke-Wiegand counterexample

Son Pham publicly identified a counterexample to the Huneke-Wiegand conjecture in the class of two-generated monomial ideals over symmetric numerical semigroup rings, subsequently verified independently by Professor Craig Huneke. This preprint preserves that discovery priority an...

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

Paper B of a three-paper research record. The two-variable Jacobian conjecture remains open after the 2026 counterexample in dimension 3. This paper develops an exact-arithmetic campaign on the lone open degree pair (72,108) below 125, built on Guccione-Guccione-Horruitiner-Valqu...