Authors: Sofiia Ivanko, & Peter Farag*
Published Date: 25 March, 2025
Cite: Ivanko and P. Farag, “Proof of the Riemann Hypothesis and the Modified Collatz Conjecture Using the Sophy-Peter Mathematical Framework,” Crystal Journal of Artificial Intelligence and Applications, vol. 1, no. 1, p. 01-33, 2025.
Abstract
In this article, we present solutions for one of the oldest mathematical problems, the Collatz Conjecture, and provide a proof for the Riemann Hypothesis, utilizing a new number theory based on newly discovered number properties, which will also be presented in this paper. This became possible through the Sophy-Peter mathematical framework, built upon this new number theory. The Collatz Conjecture will be disproven, but as an alternative, the Oscillating Theorem will be introduced, with its correctness proven within this article. Furthermore, we present the general version of the Riemann zeta function, developed based on the new number theory. The correctness of this function is verified by comparing it with existing results of the zeta function. Using this approach and the Sophy-Peter framework, we have successfully proven the Riemann Hypothesis, long considered a millennium problem. Moreover, since the general zeta function is proven, this implies the correctness of the new number theory and the Sophy-Peter framework.
Keywords
Sophy-Peter Framework, New Number Theory, Modified Collatz Conjecture, Oscillating Theorem, General Zeta Function, Proof of the Riemann Hypothesis
Authors: Siddarth Laxminarayanan*
Published Date: 05 June, 2025
Cite: S. Laxminarayanan, “The Convergence of Quantum Computing and AI in Defence: Shaping the Future of Global Security,” Crystal Journal of Artificial Intelligence and Applications, vol. 1, no. 1, pp. 01–06, 2025.
Abstract
Quantum Computing (QC) and Artificial Intelligence (AI) are emerging technologies poised to significantly transform global defense strategies. With exceptional computational capabili-ties, Quantum Computing has profound implications for military cryptography and secure communications, potentially altering national security paradigms. Simultaneously, Artificial Intelligence contributes advanced predictive analytics, strategic modeling, and autonomous system functionalities, enhancing real-time intelligence and operational effectiveness in mili-tary contexts. This convergence between QC and AI offers unprecedented opportunities for strengthening defense systems; however, it also introduces critical challenges related to cyber-security vulnerabilities, ethical considerations in autonomous military operations, and complex geopolitical tensions. Utilizing scenario planning, this article examines three plausible future scenarios: the High-Integration scenario, depicting rapid and comprehensive incorporation of QC and AI into military systems; the Regulated-Adoption scenario, emphasizing international regulations and collaborative oversight mechanisms; and the Ethical Constraints scenario, highlighting stringent ethical guidelines limiting certain military applications. Each scenario illustrates distinct shifts in military capabilities, cybersecurity posture, and the dynamics of autonomous system deployment, while emphasizing the necessity for robust governance frameworks. Moreover, the study underscores the essential role of international collaboration and comprehensive ethical guidelines in responsibly navigating the potential benefits and in-herent risks associated with these advanced technologies. Ultimately, managing the integra-tion of Quantum Computing and Artificial Intelligence within defense sectors effectively requires proactive global cooperation, strategic regulatory frameworks, and ethical oversight to safeguard international security and stability.
Keywords
Quantum Computing, Artificial Intelligence, Governance, Ethics, Defence Technology, Mili-tary Strategy, Global Security, Cryptography, Autonomous Systems
Authors: Mauro Grassi*, & Valeria Rondoni
Published Date: November 10, 2025
Cite: M. Grassi and V. Rondoni, “A Chatbot Project to Educate and Inform Citizens about Territorial Risks,” Crystal Journal of Artificial Intelligence and Applications, vol. 1, no. 1, pp. 01-09, 2025.
Abstract
The paper examines the application of artificial intelligence (AI) and chatbots in the public sector, focusing on territorial resilience and civic participation, especially in natural risk management. The benefits of AI, such as cost reduction and improved services, are explored, providing numerous examples of success in the public and private sectors. Despite the benefits, the paper highlights significant obstacles to adoption, including citizen distrust and privacy concerns. Finally, the paper presents the CHAT-PART project, which proposes the use of chatbots to improve communication and citizen engagement in planning resilient communities, highlighting the importance of a useful and conversational design for these tools and the need for an inclusive implementation that respects the values of public service.
The increasing adoption of Artificial Intelligence (AI) and chatbots in the public sector holds significant promise for enhancing citizen services, improving communication between government and citizens, and reducing administrative burdens. AI-based chatbots, defined as intelligent agents capable of understanding spoken language and automating communications, can offer benefits such as cost savings, increased productivity, and improved citizen satisfaction. However, their implementation faces challenges, including public distrust in machine intelligence and ethical/social obstacles related to the replacement of human employees.
Empirical research highlights varied public perceptions and implementation challenges. An experimental online survey in Japan indicated lower initial public trust in chatbot responses for sensitive areas like parental support compared to less sensitive ones like waste separation.
Studies on US state governments identified key determinants for chatbot adoption, such as relative advantage, ease of use, dynamic interactions (especially driven by the COVID-19 pandemic), leadership, and past experiences. Implementation success, conversely, is influenced by knowledge base creation, technological expertise, human and financial resources, inter-agency communication, privacy regulations, and citizen expectations. A Greek study validated AI integration into public service delivery through application scenarios in collaboration with government agencies.
Crucially, AI-based chatbots are highly applicable to risk education and management for territories. The CHAT-PART project is specifically designed to leverage this potential by building a participatory planning model for climate change adaptation and natural risk resilience. This paper aims to address the critical need for continuous, widespread, and informed citizen participation in risk governance, moving beyond traditional, often overly technical, one-way information dissemination. By focusing on specific multi-risk territories in Italy, CHAT-PART seeks to integrate specialized chatbots to foster information, training, and involvement of the population in policies and actions against natural risks, contributing to the realization of a "Good AI Society" by addressing research gaps in public trust and engagement.
CHAT-PART Project (Participatory Planning Model): This project aims to develop and validate a "participatory planning model" for local adaptation to climate change and natural risks. This model will:
Be agreed upon and calibrated with selected Italian municipalities.
Be presented to local citizens and media to gather feedback and technical/institutional specifications.
Incorporate a specialized chatbot designed to facilitate information, training, and broad citizen participation in the planning and management of natural risks.
Be proposed and implemented in four different municipalities (Marradi, Genoa, Ercolano, Viareggio) with varying sizes and risk types, allowing for real-world testing and assessment of its effectiveness in fostering participation.
Involve an initial research phase on chatbot use to facilitate citizen-government interactions, including through surveys and feedback.
Include a phase for developing recommendations for building a citizen participation model.
Plan for subsequent initiatives to discuss the general proposal within institutions and with citizens in different territories.
Keywords
Artificial Intelligence (AI), Chatbots, Public Sector/Government, Citizen Services, Public Trust, Risk Education, Territorial Risk Management, Climate Change Adaptation, Participatory Planning, Innovation Adoption, Digital Transformation
