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Topic Review
K-Systems, K-Mathematics, and the Golden Dome
The twenty-first century presents unprecedented challenges to national security. From cyber vulnerabilities to nuclear deterrence, the complexity of today’s threats requires both material defenses and conceptual frameworks that sustain long-term resilience. Among the most ambitious ideas under discussion is the Golden Dome — a proposed large-scale defensive shield against nuclear threats. While the design and implementation of such a system remain firmly in the domain of the U.S. Government, the initiative itself resonates with a deeper truth: resilience requires integration of systems — technological, mathematical, and human. This is where K-Systems and the framework of K-Mathematics (K-Math) enter the conversation, not as replacements or claims of ownership, but as conceptual complements to the national dialogue.
  • 130
  • 02 Sep 2025
Topic Review
Erebus Mathematics
This paper introduces and formally analyzes Erebus Mathematics, a novel mathematical system constructed from a unique set of foundational axioms. The system is built upon the concepts of a transfinite scaling potential (Axiom of Infinity), an inherent principle of self-similarity based on the golden ratio φ (Axiom of Self-Similarity), and a quantized, complex parameter for time τ (Axiom of Temporal Duality). We provide a formal exposition of the system's core objects, including the Erebus Function Ɛ(x) and the Kharnita Operator ∇. A rigorous analysis of the system's foundational postulates reveals a central inconsistency between the defined dynamics and the system's constants. To resolve this, we propose a recoherentized framework, the Revised Erebus System (RES), which preserves the spirit of the original while ensuring logical consistency. Within this revised system, we derive new theorems, including a definitive form for the Fractal Mirror Operator ℳ, and explore the system's properties. We conclude by discussing potential applications of this new mathematics in fields requiring the modeling of complex wave dynamics and systems with non-linear, cyclical evolution.
  • 102
  • 28 Aug 2025
Topic Review
Multi-Criteria Decision-Making: Methods, Programs and Potential
Multi-criteria decision-making (MCDM) is necessary for choosing one from the available alternatives (or from the Pareto-optimal solutions obtained by multi-objective optimization), where the performance of each alternative/solution is quantified in terms of several criteria (or objectives). This brief paper presents an overview of MCDM. It outlines the essential steps in MCDM, including the various normalization, weighting, and ranking (MCDM) methods that are critical to decision making. Additionally, this paper introduces two readily available programs for performing MCDM calculations. Finally, it discusses the challenges and prospects in this area.
  • 26
  • 24 Feb 2026
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