Research works

A Class of Regularization Schemes for Linear Ill-Posed Problems in Banach Spaces Under Low Order Source Conditions

In this work we consider, in a Banach space framework, the regularization of linear ill-posed problems. Our focus is on the recovery of solutions that have a logarithmic source representation. Such cases typically occur in exponentially ill-posed problems like the backwards heat...

Defect Flow, Incidence Rank, and Boundary Descent for Seymour's Second-Neighborhood Conjecture

We develop a degree-independent structural toolkit for Seymour's second-neighborhood conjecture. The main contributions are block and trap defect factorizations, arbitrary-baseline total-defect balance, protected-parent and Hall-deficiency separator geometry, Boolean defect flow...

SGBS-00: SETT Governance Benchmark Series: Overview and Methodology

This document defines the common methodology for the SETT Governance Benchmark Series (SGBS), a set of four controlled benchmarks and one adversarial stress test. The series evaluates a specific architectural question: what cost and what tested evidence arise when probabilistic r...

Observability Is Not Enforcement: A Doctrinal Framework for Distinguishing Compliance Instrumentation from Runtime Authorization in AI Governance Architectures (Working Paper v2.0)

AI compliance instrumentation can produce extensive evidence without controlling whether a governed action occurs. Many contemporary systems embed explainability artifacts, monitoring dashboards, drift detection, and integrity-protected audit bundles into development pipelines, i...

Four-Dimensional Pure Yang–Mills Theory: Wightman Construction and Mass Gap for Compact Connected Gauge Groups with Simple Lie Algebra

For every compact connected non-abelian gauge group with simple Lie algebra, including every finite central quotient as a distinct global form, this paper constructsa nontrivial pure Yang–Mills Wightman quantum field theory on R 4 with a unique invariant vacuum and a strictly pos...

Beyond Babel: What Remains When No Certainty Remains — An Introduction to Reflexive Minimalism

An essayistic introduction to a philosophical project grounded in epistemic finitude, written for readers without formal philosophical training. It begins from a contemporary predicament: we have never communicated more and rarely understood one another less, while nuclear weapon...

Antimatter as Reverse-Cascade: A Geometric Resolution of the Dirac Time-Reversal Paradox in Fractal Mechanics

The Dirac equation predicts antimatter as negative-energy solutions equivalent to particles propagating backward in time — an interpretation that has remained physically unsatisfying for 95 years. We propose a geometric resolution within Fractal Mechanics (FM): antimatter is not...

From Symmetry to Invariance: Learning Galois Equivalent Representations in Finite Fields

Neural networks can learn algebraic operations from finite examples,but it remains unclear whether this ability transfers acrossmathematically equivalent representations of the same operation. Westudy this question through multiplication in finite fields underchanges of basis. Th...

The Digital Road Method: A Neutral Analysis of Structural Syntax, Modulo-9 Reduction, and Document Object Architecture in the Quranic Matrix

Abstract This paper presents a rigorous computational and theoretical evaluation of text conceptualized as an engineered data matrix, utilizing the Digital Road Method. By mapping the syntactic and structural boundaries of ancient Semitic text structures against the backend docum...

Unveiling the Structure of Cayley-Dickson Algebras: Zero Divisor Counting and Listing, and a Novel Sign Compression Scheme

This paper presents a comprehensive computational and empirical investigation into the structure and properties of Cayley-Dickson algebras ($A_x$, dimension $2^x$). We establish and validate an explicit formula, $N(x) = \frac{(2^x - 2)(2^x - 4)(2^x - 8)}{16}$, which accurately en...

Bridging the Interpretability Gap: A Comparative Review of Regulatory Trends and Technical Implementations of Explainable AI (XAI) in the Financial Systems of Emerging Economies

As financial institutions transition from traditional statistical models to complex "black-box" AI systems, the demand for transparency has created a critical interpretability gap. This paper provides a comparative review of the regulatory trends and technical implementations of...

Low-Rank Segre Geometry, Automorphism Groups, and Complement Cohomology of a Binary Two-Step Algebra

This paper determines the intrinsic geometry, symmetry structure, and complement cohomology of an explicit forty-three-dimensional two-step nilpotent associative algebra over the binary field and of its associated algebra group. The contraction ranks of the induced quadratic map...

Language-Mediated Belief/Behavior Attractors in Human-AI Interaction: A Mechanism and Defensive Architecture for AI Mind-Virus Phenomena

We examine how large language models can participate in the propagation of language-mediated belief/behavior attractors — self-reinforcing patterns of interpretation that move through human-agent conversation and shape what people believe and do. The mechanism is not biological c...

Artificial Intelligence in Healthcare. A review of recent trends, applications, challenges and future directions

Artificial intelligence (AI) is becoming an important technology in modern healthcare because of its ability to analyze large volumes of clinical, biomedical, and patient-generated data. AI-based systems are being applied in disease diagnosis, medical imaging, drug discovery, per...

Explainable AI in Healthcare: A Comparative Analysis of Interpretability Techniques for Clinical Decision Support Systems

Artificial intelligence has made a great impact on healthcare by providing accurate disease diagnosis, personalised treatment regimens, and efficient clinical decision making. But many of the advanced machine learning and deep learning models are black-box systems, and healthcare...

The Cover-up of a Terrorist Incident by the 'United Kingdom Government'

This document is "The Cover-up of a Terrorist Incident by the 'United Kingdom Government'", authored by Graham Edwin Wilkins. It serves as a comprehensive record of the author's attempts to report and seek assistance regarding a sustained campaign of alleged crimes committed agai...

Response Quotients for Exact Semantic Representation

Given a state space, admitted interface space, outcome space, and response map, we identify states that agree under every admitted query. The resulting response quotient carries a uniquely descended Full Admitted Response. We define response spaces and response-equivalence-preser...

The Cover-up of a Terrorist Incident by the 'United Kingdom Government'

This document is "The Cover-up of a Terrorist Incident by the 'United Kingdom Government'", authored by Graham Edwin Wilkins. It serves as a comprehensive record of the author's attempts to report and seek assistance regarding a sustained campaign of alleged crimes committed agai...

A Chloroplast-Inspired Theranostic Nanoplatform for Self-Sustaining Oxygen-Elevating Photodynamic Therapy and Glutathione-Triggered Carbon-Centered Radical Synergistic Therapy

Achieving precise drug delivery to the tumor site can minimize systemic side effects caused by off-target effects. As a therapy that depends on oxygen content, photodynamic therapy (PDT) is significantly constrained by the hypoxic nature of the tumor microenvironment (TME). Compa...

Discrete Derivation of the Fano Plane from the Non-Freezing Principle

This paper establishes, within the discrete regime of the Triniton framework, that the non-freezing filter MP(III) — the third constitutive component of the Meta-Principle — together with the selection filters N1–N4, P-admissibility, Class A, and a lexicographic CPE refinement, f...