Research works

The Transformation of Human Communication in the Digital Age: A Narrative Review of Technological Connectedness, Empathy, and Meaningful Relationships

The integration of digital technologies into everyday life has profoundly reshaped the forms, pace, scope, and meaning-making processes of human communication. Interpersonal interaction is no longer confined to face-to-face settings; it increasingly unfolds through social media p...

Beyond Delegation Depth: Audit Reach, Enforcement Reach, and Management Coverage in Recursive AI Delegation

Recursive AI delegation is commonly constrained by hop counts, but equally deep structures can differ in whether authority remains attributable, auditable and stoppable. This paper separates path-level management-substrate coverage from contiguous audit reach, structural enforcem...

Interactive Pedagogical Strategies for Enhancing Student Engagement in Online Christian Higher Education

Student engagement is a crucial concern in Online Christian Higher Education (OCHE), where learning is expected to be both academically rigorous and formational. While interactive pedagogical strategies are widely recognised as critical to effective online learning, existing enga...

Invariant Speed of Light in a Continuous Physical Substrate: A Three-Dimensional Material Derivation of Local c Invariance, Clock Dilation, and Gravitational Redshift

This paper presents a three-dimensional material-coordinate derivation of local propagation-speed invariance for an observer physically embedded in a continuous physical substrate. Starting from a barotropic continuum description, mass conservation, and an exact finite-deformatio...

REIMAGINING VOCAL PEDAGOGY: A COMPETENCY-BASED FRAMEWORK FOR SINGER FORMATION

Contemporary singer education continues to be largely grounded in traditional models of vocal pedagogy that prioritize technical proficiency and artistic performance. While these foundations remain indispensable, the evolving realities of twenty-first-century musical practice dem...

Branching Cascades in Hierarchical Coordination Systems: Criticality Conditions, Finite-Depth Effects, and Tests of Geometric Scaling

Hierarchical coordination can support branching cascades, but regulated load does not establish critical reproduction. The paper distinguishes independently measured load, offspring transmission, boundaries and observation rules. Classical critical Galton-Watson theory supplies t...

A Cervicogenic Mechanical–Glymphatic Shared Subtype Hypothesis of Bipolar Depression: A Theoretical Extension Based on the Investing Fascia–Carotid Sheath–Six-System Coupling Framework

Depressive episodes in bipolar disorder (BD) and major depressive disorder (MDD) overlap considerably in clinical presentation, making differential diagnosis challenging. Existing models have largely focused on central and molecular levels, with little systematic investigation of...

Riemann Minimal Entropy Collapse - A Topological Proof by Contradiction of Non-Trivial Zeros via Spectral Rigidity in Lean 4 & Comparator

This paper presents a machine verified topological proof by contradiction of the Riemann Hypothesis via spectral rigidity. Departing from brute-force numerical sweeps and isolated analytic approximations, we establish a foundational topological equivalence ($\infty \sim 0$ on ${R...

Mercator 2.0: The PTCt Relational Framework and a First Equal-Area Projection Profile (PTCt-1)

Mercator 2.0 / PTCt is an exploratory relational cartographic framework that separates the physical Earth model, projection-independent geographical relations, and planar representation. The framework defines four components: Skin (P), a dimensionless measure of relative surface...

Cosmological General Relativity Black Holes: A Consolidated and Independently Verified Treatment of Kerr and Kerr-Newman Dynamical Embedding

This paper consolides and fixes the definitive status of the conformal embedding, of Kerr and Kerr-Newman black holes in Cosmological General Relativity (CGR), superseding several earlier drafts in which corrections established by independent verification were repeatly omitted on...

Attention Economics in the Age of Artificial Intelligence: The Impact of Algorithmic Groove Music Recommendations on Social Media Users

This research examines the relationship between groove-oriented short-form video content, user engagement behavior, and recommendation-driven consumption in social media environments. The study combines a within-subject video experiment with an international survey to investigate...

Structural Vulnerability in Hierarchical Networks: A Dependency-, Redundancy-, and Level-Aware Framework and Its Empirical Limits

Classical node-importance measures (degree, betweenness, closeness, eigenvector, PageRank, k-core) are defined solely as functions of the adjacency structure of a graph and, by construction, contain no term for hierarchical level, dependency direction, or the horizontal-versus-ve...

A Twelve‑Dimensional Ontological Manifold with Post‑Dimensional Completion, Exhaustion Structures, and the Unified Carlo Meta‑Ontic Operator

This upload contains the complete formal document **“A Twelve‑Dimensional Ontological Manifold with Post‑Dimensional Completion and Exhaustion Structures”** together with its accompanying **one‑page Carlo Engine summary**. Together, these works present the full architecture of th...

THEOLOGICAL FORMATION OF VOCAL IDENTITY IN DIGITALLY MEDIATED WORSHIP: DEVELOPING A CONTEXTUAL FRAMEWORK FOR AFRICAN WORSHIP LEADERSHIP

The rapid expansion of digitally mediated worship has significantly reshaped Christian worship leadership, creating new opportunities for ministry while raising important theological, pedagogical, and contextual questions regarding the formation of worship leaders. Although exist...

KOKU Anomalous-Force Question Cascade: A Factorial Digital Laboratory for Momentum-Channel Falsification

This technical note turns a speculative non-reaction-propulsion question into a sequence of falsifiable questions. Seven candidate theory classes are screened by momentum-channel accounting. A randomized 256-block factorial design separates a declared device-fixed anomaly signatu...

Sharp Closure Thresholds for Two-Hidden-Layer ReLU Networks

Preprint, Version 1. This manuscript has not been peer reviewed. This deposit establishes a public, citable, version-specific scholarly record of the manuscript and its accompanying source and verification materials. No journal acceptance or endorsement is implied. The SHA-256 ch...

Nonclosed powers of a Zariski-closed subset of GL₃ in characteristic five

We construct a Zariski-closed subset \(Y\) of \(\mathrm{GL}_3(\overline{\mathbb F_5(u)})\) containing the identity such that \(Y^m\) is not closed for every integer \(m\geq2\). The same diagonal matrix lies in \(\overline{Y^m}\setminus Y^m\) for all such \(m\). The construction u...

Collocation and Green Functions for Elliptic Interface Problems

This deposit contains the complete recorded numerical evidence for: *Benefits and limits of physics-informed point allocation for elliptic interface problems: Controlled RBF-FD, adjoint, and Robin-coupling comparisons* It includes the production and holdout archives for controlle...

The Transformation of Human Communication in the Digital Age: A Narrative Review of Technological Connectedness, Empathy, and Meaningful Relationships

The integration of digital technologies into everyday life has profoundly reshaped the forms, pace, scope, and meaning-making processes of human communication. Interpersonal interaction is no longer confined to face-to-face settings; it increasingly unfolds through social media p...

A universal 23-dimensional realization of Steiner triple codes

For every finite complete Steiner triple system, we construct bounded full-dimensional strictly convex compact sets in 23-dimensional Euclidean space whose code and interior code are exactly the associated Steiner triple code. Three simultaneous quadratic coefficient relations re...