Felipe A. Santibáñez-Leal

The first interior shell of the Bougard-Joret extremal problem

Let f(n, α, k) be the minimum size of a k-connected graph of order n and independence number α. Das and Gupta recently determined the boundary n = α + k and disproved the proposed Bougard-Joret formula there. We determine the entire admissible first interior shell: f(α + k + 1, α...

Domain Walls Become the Optimal Reversal of a Spin Chain: Free Optimal Control Beyond the Macrospin and an Energy-Barrier Floor on the Switching Cost

Optimal control of magnetization switching has been solved almost entirely for a single rotating moment, and its authors state in print that it remains open under what conditions nonuniform mechanisms such as domain-wall nucleation and propagation become optimal in terms of energ...

The Cost of Reliability in Optimal Magnetization Switching: A Longitudinal-Field Front for Van der Waals Magnets

Optimal control theory delivers magnetic-field pulses that reverse a magnetic moment for the least dissipated energy, and recent work shows these pulses reach picosecond, energy-efficient switching in two-dimensional van der Waals magnets. Because the optimal pulse is always perp...

Uniform Rotation is the Field-Cost Optimum over a Domain-Wall Sweep: A First Step Beyond the Macrospin in Optimal Magnetization Switching

Optimal control of magnetization switching has been solved almost entirely at the macrospin level, where the magnetic element is a single rotating moment. The authors of the method state, in print, that this approximation breaks down with size and that the reversal may proceed by...

Simple critical zeros in short intervals: stability, pressure, and parity

We study proportions of simple and distinct nontrivial zeros of the Riemann zeta function in short intervals. The finite stable Hilbert rank-trace method and Wang's fixed-test short-interval input are retained with their stated assumptions. An odd-multiplicity parity transfer com...

The first interior shell of the Bougard-Joret extremal problem

Version 0.02 proves the entire admissible first interior shell: for every integer k at least 3 and every independence number a from 2 through k+1, the minimum size of a k-connected graph of order a+k+1 and independence number a is ceiling(k(a+k+1)/2). The construction combines cl...

A quadratic family of integral two-torsion classes in a Huneke-Wiegand Koszul presentation

For every integer p>=8, we prove that an explicit integral Koszul presentation associated with a previously constructed Huneke-Wiegand family has a direct summand (Z/2)^q, where q=floor(((p-2)^2+3)/12). The classes are indexed by the strictly increasing nonnegative triples i<j

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...

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...

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 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...

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...