Open University of Cyprus

Exact replication and screening of tropical finiteness certificates for central configurations

We report an exact, fully reproducible replication and screening study around Smale's 6th problem (finiteness of planar central configurations), with the following contributions: (i) an exact calibration of the Albouy–Chenciner mutual-distance equations in open tooling, including...

oreblocks: License-Free Synthetic Ore-Body Block Models with a Stamped Exact Ultimate-Pit Optimum

Benchmarking an open-pit optimiser, a mine-dispatch simulator, or a teaching tool needs realistic ore-body block models with a known answer, but the standard public instances (the MineLib library) are granted for academic download only and cannot be redistributed, and real mine m...

Planar Keller Maps after the Counterexample: Machine-Certified Newton-Polygon Exclusions, the Staircase Transport, and the Recalibrated Frontier

The July 2026 counterexample settled the Jacobian conjecture in dimensions N ≥ 3 and left JC(2) as the open case. This paper develops an exact-arithmetic program on the planar case. The Keller condition J(P, Q) = 1 is linear in Q for fixed P; the resulting machine (eliminate, par...

Leakage-Free Operational Earthquake Forecasting: A Multi-Region CSEP Testbed with Pre-Registered Negative Results and the Horizon-Dependent Value of Geodetic Context

Operational earthquake forecasting (OEF) issues calibrated conditional probabilities of future seismicity; the Epidemic-Type Aftershock Sequence (ETAS) model is its de-facto benchmark, and under fair, prospective, CSEP-style testing no machine-learning temporal point process has...

Physics-Informed Reconstruction of Unmeasurable Cardiac Fields from Real Data: Electrocardiographic Imaging and 4D-Flow Aortic Pressure, Verified Against Known Answers, with Null Results

Two clinically decisive cardiac quantities cannot be measured where they are needed: the heart-surface potential map (measured only with an invasive electrode cage) and the intra-vascular pressure field (measured only with a catheter). Each is tied by a governing equation to a qu...

Dual-Representation Mondrian Conformal Assignment of Pressure-Transient GeoTypes: An Independent Reproduction and Extension for Fractured-Reservoir Flow

Fractured reservoirs exhibit recurring fluid-flow behaviours hidden in the shape of their pressure-transient responses. A recent study clusters geologically consistent discrete-fracture-network (DFN) ensembles into flow-behaviour classes and attributes each class to fracture-netw...

Frobenius Minimality, Minimum-Layer Uniqueness, and an Infinite Family of Huneke-Wiegand Counterexamples

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 by Professor Craig Huneke. We preserve that discovery priority and answer two different que...

minehaulsim: A Deterministic Discrete-Event Simulator of Mine Haulage on a Constrained Road Network

The productivity of an open-pit mine is set at the truck-shovel interface, where a fleet of haul trucks cycles between shovels and dumps over a road network of ramps, junctions and single-lane segments. Simulating that interface faithfully needs the network: travel times depend o...

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...

One Image, Twelve Mathematics: A Cross-Family Benchmark and the U-Shaped Editability of Image Representations

An image is always a matrix, but it can be re-expressed in many ways: as a sum over a Fourier, cosine, or wavelet basis, as a sparse combination of atoms from an overcomplete dictionary, as a handful of geometric primitives, as a small neural function of position, as an explicit...

Prequential Streaming Evaluation of Stateful Time-Series Forecasters with Online Conformal Calibration: A Diagnostic Atlas and the preqts Harness

Real forecasting is streaming: observations arrive one by one, the model updates, and its prediction intervals must stay calibrated as the series drifts. Yet every widely used forecasting benchmark harness evaluates models statelessly on rolling windows, carrying no state across...

Keeping the Whole Model Family: Bootstrap-Aggregated Phenomenological Ensembles for Mining and Industrial Process Data

Industrial practice fits a family of candidate phenomenological models to process data and then keeps one winner, selected by R2 or an information criterion. That discards the evidence about model form and leaves the reported prediction without the uncertainty that model form car...

The Jacobian Conjecture after the Three-Dimensional Counterexample: Exact Validation, a General Seed Family, the Geometry of Non-Properness, and Two-Dimensional Equivariant Rigidity

On 2026-07-20, Levent Alpöge announced (crediting the language model Claude Fable 5 and a question posed by Akhil) an explicit polynomial map F from C^3 to C^3 with constant Jacobian determinant -2 and a repeated value, refuting the Jacobian conjecture for every N ≥ 3. We report...

pygeotypes: A Dependency-Light Shape-Catalogue Library with Class-Conditional Conformal Assignment for Physical Response Signals

Many physical systems are characterised through the shape of a response signal: the pressure transient of a fractured reservoir, the drawdown of a hydrogeology pumping test, the temperature curve of a thermal-response test. A recent methodology, GeoTypes (Kamel Targhi et al., 202...

A Band-Mask Robustness Diagnostic for Latent Dirichlet Allocation on Hyperspectral Imagery

Latent Dirichlet Allocation (LDA) and its neural variants are increasingly used as interpretable spectral mixture models on hyperspectral imagery. Their seed and capacity stability has been studied at length; their robustness to the choice of spectral window has not. We introduce...

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...

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...

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 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...