Open University of Cyprus

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

We study an explicit integral Koszul presentation arising in the graded-syzygy analysis of a previously constructed Huneke-Wiegand family. For every integer p>=8, its cokernel contains a direct summand isomorphic to (Z/2)^floor(((p-2)^2+3)/12). The classes are indexed by strictly...

Simple critical zeros in short intervals: stability, parity, localization, Hilbert compression, and spectral defect

For a conjugation-invariant finite multiset, let N count copies, S simple real support, O distinct odd-multiplicity real support, Q the squared-kernel pair sum, and D(G)=tr Psi_2(G) the retained simple-real Gram spectral defect. The paper proves the finite inequality (Q-S-D(G))(N...

Simple critical zeros in short intervals: stability, parity, localization, Hilbert compression, and spectral defect

For a conjugation-invariant finite multiset, let N count copies, S simple real support, O distinct odd-multiplicity real support, Q the squared-kernel pair sum, and D(G)=tr Psi_2(G) the retained simple-real Gram spectral defect. The paper proves the finite inequality (Q-S-D(G))(N...

Action-Conditioned Latent Dynamics for Mineral Processing: A World-Model Engine, and a Measured Account of Where It Earns Its Cost

A forecaster maps history to a future. A world model maps history and a proposed action sequence to a distribution over futures. That single difference is what makes counterfactual questions, planning and regime detection expressible at all, and it is the difference this paper is...

Simple critical zeros in short intervals: stability, parity, localization, and Hilbert compression

For a conjugation-invariant finite multiset, let N count copies, S simple real support, O distinct odd-multiplicity real support, and Q the squared-kernel pair sum. The paper proves the sharp inequality (Q-S)(N-O) >= 2(N-S)^2 by retaining Lamzouri's first Hilbert-subspace dimensi...

Action-Conditioned Latent Dynamics for Mineral Processing: A World-Model Engine, and a Measured Account of Where It Earns Its Cost

A forecaster maps history to a future. A world model maps history and a proposed action sequence to a distribution over futures. That single difference is what makes counterfactual questions, planning and regime detection expressible at all, and it is the difference this paper is...

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

We study an explicit integral Koszul presentation arising in the graded-syzygy analysis of a previously constructed Huneke-Wiegand family. For every integer p>=8, its cokernel contains a direct summand isomorphic to (Z/2)^floor(((p-2)^2+3)/12). The classes are indexed by strictly...

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

Let C3 = 0.6567752140190419405677628751089899133... be the reproducible rank-three optimized Selberg constant. For every fixed 1/2 < theta < 1, localization of the Selberg detector to (T,T+Ttheta] gives a lower asymptotic proportion (theta-1/2)/(4eC3) of distinct odd-multiplicity...

Post-hoc Interpretability of LDA on Hyperspectral Imagery: SHAP Attributions, Counterfactual Topic Flips, and LLM-judge Alignment under Token-Mass-Dispersion Asymmetry

The interpretability claim of LDA-on-HSI rests on the assumption that topic-word distributions are human-readable. This study is restricted to the LDA backbone; the cross-backbone comparison (HDP, ProdLDA, ETM) is the subject of the companion paper P4. We test three orthogonal po...

Which Backbone Picks Which Wordification? A Factorial Study of Topic-Model Families on Hyperspectral Imagery

The companion paper (P3) showed that nineteen wordification recipes (V1-V15, V17-V20) produce measurably different topic bases under a fixed LDA backbone, with no universal winner: V12 (Gaussian-mixture tokens) has the highest mean coherence and topic-label coupling (winning two...

Post-hoc Interpretability of LDA on Hyperspectral Imagery: SHAP Attributions, Counterfactual Topic Flips, and LLM-judge Alignment under Token-Mass-Dispersion Asymmetry

The interpretability claim of LDA-on-HSI rests on the assumption that topic-word distributions are human-readable. This study is restricted to the LDA backbone; the cross-backbone comparison (HDP, ProdLDA, ETM) is the subject of the companion paper P4. We test three orthogonal po...

Beyond Accuracy: A Multi-Axis Evaluation Framework for Interpretable Topic Models on Hyperspectral Imagery

Topic models, in particular Latent Dirichlet Allocation (LDA), have been adapted to hyperspectral imagery (HSI) as a route to interpretable spectral mixtures: each spectral unit (canonically a pixel) becomes a document of quantised band-frequency tokens and the inferred topic-wor...

Which Wordification Matters? A Nineteen-Recipe Sweep of the Interpretable-Topic-Model Framework on Hyperspectral Imagery

The companion paper (P1) introduces a twelve-axis evaluation framework for topic models on hyperspectral imagery and instantiates it on a single canonical wordification recipe (V1, band-frequency tokenisation). This paper asks a different question: how does the choice of wordific...

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...

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...

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...

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...

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...

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...

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...