Felipe A. Santibáñez-Leal

The Bottom of the Shub–Smale Tau Conjecture: an Exact Census of Integer Roots for Constant-Free Straight-Line Programs of Length at Most Eight

For a univariate integer polynomial f, let τ(f) be the minimum number of +, -, × 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 + τ(f))^κ f...

An independent exact verification of the 2026 counterexample to Goemans' unsplittable-flow cost conjecture, with the violation constant it forces

In July 2026 a counterexample to Goemans' cost version of the Dinitz–Garg–Goemans theorem was announced publicly, outside peer review, and circulated widely. We report an independent verification of that finite object by exact rational enumeration, performed without executing or...

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...

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...

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...

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...

beltvision: A Reproducible Classical Computer-Vision Inspection Engine for Conveyor Belts, Verified on Ground-Truth Synthetic Scenes

Conveyor-belt inspection asks a vision system to find the belt, measure its geometry, tell an empty return strand from a loaded one, and flag damage or foreign objects, and the practical difficulty is that most published demonstrations run on private field footage that no one els...

Atalaya: A Calibrated Multi-Evidence Affinity Graph over an Open-Data Catalog, with a Shuffled-Alignment Negative Control for False Discoveries

Open-data portals publish thousands of datasets as a flat searchable list, but the relational knowledge that makes the data useful, which datasets can be joined, which describe the same thing, and which actually correlate when aligned by a common key, stays implicit and is infeas...

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...

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...

Curvilinear Geometry, Primary Structure, and Gröbner Degenerations of Conductor Fiber Cones in a Huneke–Wiegand Family

For every integer p>=4, a previously constructed symmetric numerical semigroup ring R_p and rigid two-generated monomial ideal determine a conductor ideal T_p whose special fiber C_p = F(T_p) is one-dimensional Cohen-Macaulay, generated in degree one by 10p monomials, and has mul...

The Collateral Impact of the Three-Dimensional Jacobian Counterexample: a Source-Verified Cascade

On 2026-07-20, Levent Alpöge announced an explicit counterexample to the Jacobian conjecture in dimension 3, found working with the language model Claude Fable 5 (Anthropic). The credit for every consequence documented here belongs to that single map. This paper documents what el...

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...

milldem: A Cross-Platform Soft-Sphere DEM for Tumbling-Mill Charge Motion and Size-Consistent Net Power

The discrete element method (DEM) is the standard tool for simulating charge motion and power draw in tumbling mills, but the mature open engines that do it well (LIGGGHTS, YADE, the LAMMPS granular package) are C++ codes whose build on Windows effectively requires a Linux subsys...

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...