Research Article
On the Discrete and Continuous Harmonic Encoding of Primes
Ioannis Papadakis*
Issue:
Volume 11, Issue 3, June 2026
Pages:
45-56
Received:
4 April 2026
Accepted:
15 April 2026
Published:
21 May 2026
Abstract: The dichotomy between the prime-based multiplicative and additive representations of integers poses fundamental and distinct challenges in analyzing the underlying prime distribution. This paper contributes to this area of research by introducing a tripartite framework for the lossless mathematical encoding of primes and their additive partitions. First, we establish Hybrid Prime Factorization (HPF) as a bounded a priori structural prime-generation framework. On certified intervals, primality is forced by disjoint partitions of canonical prime bases under the stated magnitude bound, so that certain HPF configurations yield prime outputs structurally, i.e., without requiring a separate post hoc primality test of the evaluated output. Second, to address the linear expansion of additive partitions, we introduce a deterministic pairing map, L(N), which losslessly
compresses the entire additive state of even integer partitions into a single, uniquely factorizable scalar in ℤ. Finally, recognizing the asymptotically factorial limits of discrete integer representation, we map this arithmetic complexity into the
continuous domain. We derive bounded, piecewise smooth harmonic sieve functions over ℝ \ ℤ that isolate prime and composite structures through the limits of indeterminate trigonometric forms. This progression establishes that prime complexity need not be confined to discrete combinatorial bounds, but can be translated into continuous harmonic functions, demonstrating that the prime counting function π(x) can be generated as a sum of continuous harmonic trigonometric functions.
Abstract: The dichotomy between the prime-based multiplicative and additive representations of integers poses fundamental and distinct challenges in analyzing the underlying prime distribution. This paper contributes to this area of research by introducing a tripartite framework for the lossless mathematical encoding of primes and their additive partitions. ...
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Research Article
Agape and Algorithms: Reframing Artificial Intelligence Ethics in Africa Through Fletcherian Situational Ethics
Oviemuno Wilfred Egara*,
Bridget Gwa Oviemuno,
Charles Elijah
Issue:
Volume 11, Issue 3, June 2026
Pages:
57-63
Received:
3 April 2026
Accepted:
16 April 2026
Published:
28 July 2026
DOI:
10.11648/j.mcs.20261103.12
Downloads:
Views:
Abstract: Concerns regarding ethical issues, such as algorithmic fairness, accountability, transparency, and the preservation of human dignity, have increased due to the fast integration of artificial intelligence (AI) into a variety of global sectors. Principles like safety, explainability, and regulatory compliance are given top priority in many of the current global AI governance frameworks. The sociocultural, historical, and communal dynamics that are common in African communities may not be sufficiently accommodated by these methods, which are frequently drawn from Western intellectual traditions. The potential of situational ethics, specifically, Joseph Fletcher's agape-focused framework, as a further lens for evaluating AI systems in African contexts is examined in this research. Employing the hermeneutic method of inquiry, the topic illustrates how situational ethics’ fundamental components: pragmatism, relativism, positivism, and personalism, can promote context-sensitive assessments of AI through conceptual analysis. This viewpoint emphasizes human and communal well-being over rigid regulations, placing agape (selfless, other-oriented love) as the paramount norm. It provides a way to align AI deployment with African relational and communitarian values, such as those embodied in the Ubuntu philosophy of relationality. This paper suggests that Fletcher’s agapeic framework may solve epistemic inequities in global AI discourse and fosters inclusive technology growth by fusing situational ethics with traditional African philosophies.
Abstract: Concerns regarding ethical issues, such as algorithmic fairness, accountability, transparency, and the preservation of human dignity, have increased due to the fast integration of artificial intelligence (AI) into a variety of global sectors. Principles like safety, explainability, and regulatory compliance are given top priority in many of the cur...
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